Entanglements in Quiescent and Sheared Polymer Melts

We visualize entanglements in polymer melts using molecular dynamics simulation. A bead at an entanglement interacts persistently for long times with the non-bonded beads (those excluding the adjacent ones in the same chain). The interaction energy of each bead with the non-bonded beads is averaged over a time interval $\tau$ much longer than microscopic times but shorter than the onset time of tube constraints $\tau_{\rm e}$. Entanglements can then be detected as hot spots consisting of several beads with relatively large values of the time-averaged interaction energy. We next apply a shear flow with rate much faster than the entangle motion. With increasing strain the chains take zigzag shapes and a half of the hot spots become bent. The chains are first stretched as a network but, as the bends approach the chain ends, disentanglements subsequently occur, leading to stress overshoot observed experimentally.