Entanglement in semiflexible polymer melts and solutions from simulations

The Lin-Noolandi scaling argument predicts the entanglement molecular weight from chain geometry, and is well supported by experimental results for real polymers. The argument assumes that polymers are flexible within their tubes, which fails at some point as chains become stiffer. Everaers has made a different scaling proposal, which crosses over from semiflexible chains to stiff chains as described by Morse. Everaers’ ansatz is consistent with simulation data for a range of bead-spring melts, but is not consistent with LN. In this work, we use MD simulations to explore a wide range of entangled bead-spring ring chains, to find out how entanglement properties vary with chain stiffness and concentration. To topologically equilibrate ring chains, we soften the short-range repulsive potential to allow chains to cross. We calculate entanglement properties using three techniques: chain shrinking to find the primitive path, measuring the tube diameter by the width of the “cloud” of monomer positions about the primitive path, and directly measuring the plateau modulus. As chain stiffness varies, we observe three distinct scaling regimes, suggestive of LN scaling, semiflexible chains, and stiff chains.