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MD Simulation of Supercooled Polymer Melts : Modeling of Single-Monomer Dynamics by a Continuous-Time Random Walk Approach
We present results of molecular-dynamics (MD) simulations for the dynamics of supercooled polymer melts. After an introduction to the simulation model and its ensemble-averaged properties, we analyze the dynamics of single-monomer trajectories. In the supercooled state near the critical temperature of mode-coupling theory Tc the single-monomer trajectories display long periods of localization interrupted by “fast moves”. This observation suggests a modeling by a continuous-time random walk (CTRW), i.e. by a series of random jumps separated by random waiting times. We introduce an algorithm allowing to filter the “fast moves” so as to retain only those “moves” which comply with the conditions of a CTRW. These moves are called “jumps” in the following ; the remaining analysis is based on them. As a function of temperature and chain length we then examine key distributions of the CTRW : the jump length distribution (JLD) and the waiting time distribution (WTD) for the jumps. For the equilibrium (polymer) liquid under consideration the WTD and JLD suffice to model the single-monomer dynamics by the CTRW. For the mean-square displacement (MSD) of a monomer the results of this modeling are compared with the underlying MD data. The MD data exhibit two regimes of subdiffusive behavior, one for the early alpha-process and another at later times due to chain connectivity. By contrast, the analytical solution of the CTRW yields diffusive behavior for the MSD at all times. Empirically, we can account for the effect of chain connectivity in Monte Carlo simulations of the CTRW. The results of these simulations are then in good agreement with the MD data in the connectivity-dominated regime, but not in the early alpha-regime where they systematically underestimate the MSD from the MD. It is possible that this deviation in the alpha-regime hints at correlations between the jumps, not accounted for by the CTRW approach.