Continuous-time random-walk approach to supercooled liquids. II. Mean-square displacements in polymer melts.
The continuous-time random walk (CTRW) describes the single-particle dynamics as a series of jumps separated by random waiting times. This description is applied to analyze trajectories from molecular dynamics (MD) simulations of a supercooled polymer melt. Based on the algorithm presented by Helfferich et al. [Phys. Rev. E 89, 042603 (2014)], we detect jump events of the monomers. As a function of temperature and chain length, we examine key distributions of the CTRW: the jump-length distribution (JLD), the waiting-time distribution (WTD), and the persistence-time distribution (PTD), i.e., the distribution of waiting times for the first jump. For the equilibrium (polymer) liquid under consideration, we verify that the PTD is determined by the WTD. For the mean-square displacement (MSD) of a monomer, the results for the CTRW model are compared with the underlying MD data. The MD data exhibit two regimes of subdiffusive behavior, one for the early α 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 α regime where they systematically underestimate the MSD from the MD.
Physikalisches Institut, Albert-Ludwigs-Universität, Hermann-Herder-Str. 3, 79104 Freiburg, Germany.
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J
Helfferich
Physikalisches Institut, Albert-Ludwigs-Universität, Hermann-Herder-Str. 3, 79104 Freiburg, Germany and Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, 23 rue du Loess, 67034 Strasbourg Cedex 2, France.
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F
Ziebert
Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, 23 rue du Loess, 67034 Strasbourg Cedex 2, France.
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S
Frey
Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, 23 rue du Loess, 67034 Strasbourg Cedex 2, France.
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H
Meyer
Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, 23 rue du Loess, 67034 Strasbourg Cedex 2, France.
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J
Farago
Physikalisches Institut, Albert-Ludwigs-Universität, Hermann-Herder-Str. 3, 79104 Freiburg, Germany.
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A
Blumen
Institut Charles Sadron, Université de Strasbourg, CNRS UPR22, 23 rue du Loess, 67034 Strasbourg Cedex 2, France.
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J
Baschnagel