Relaxation\nDynamics of Entangled Linear Polymer Melts\nvia Molecular Dynamics Simulations

We present an extensive analysis of the relaxation dynamics\nof\nentangled linear polymer melts via long-time molecular dynamics simulations\nof a generic bead–spring model. We study the mean-squared displacements,\nthe autocorrelation function of the end-to-end vector, <i>P</i>(<i>t</i>), the single-chain dynamic structure factor, <i>S</i>(<i>q</i>, <i>t</i>), and the linear\nviscoelastic properties, especially the shear stress relaxation modulus, <i>G</i>(<i>t</i>). The simulation data are compared\nwith the theoretically expected scaling laws for different time regimes\nof entangled melts, and with analytical expressions that account for\ndifferent relaxation mechanisms in the tube model, namely, reptation,\ncontour length fluctuation (CLF), and constraint release (CR). CLF\ninvolves a <i>t</i><sup>1/4</sup> scaling regime in the\ntime-dependence of (1 – <i>P</i>(<i>t</i>)). With increasing chain length, a gradual development of this scaling\nregime is observed. In the absence of CR, the tube model further predicts\nthat at long times, the chain dynamics is governed by one central\nquantity, the “surviving tube fraction” μ(<i>t</i>). As a result, one expects <i>S</i>(<i>q</i>, <i>t</i>) ∝ <i>G</i>(<i>t</i>) ∝ <i>P</i>(t) in that time regime. We\ntest this prediction by comparing <i>S</i>(<i>q</i>, <i>t</i>) and <i>G</i>(<i>t</i>)\nwith <i>P</i>(<i>t</i>). For both quantities,\n proportionality with <i>P</i>(<i>t</i>) is not\nobserved, indicating that CR has an important effect on the behavior\nof these two quantities. Instead, to a very good approximation, we\nfind <i>G</i>(<i>t</i>) ∝ <i>P</i>(<i>t</i>)<sup>2</sup> at late times, which is consistent\nwith the dynamic tube dilation or double reptation approximations\nfor the CR process. In addition, we calculate nonlocal mobility functions,\nwhich can be used in dynamic density functional theories for entangled\ninhomogeneous polymer blends, and discuss the effect of entanglements\non the shape of these functions.