Segment Motion in the Reptation Model of Polymer Dynamics. II. Simulations

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We present simulation data for the motion of a polymer chain through a regular lattice of impenetrable obstacles (Evans–Edwards model). Chain lengths range from N = 20 to N = 640, and time up to 107 Monte Carlo steps. For N ≥ 160, for the central segment we find clear t1/4 behavior as an intermediate asymptote. The expected t1/2 range is not yet developed. For the end segment also the tl/4 behavior is not reached. All these data compare well to our recent analytical evaluation of the reptation model, which shows that for shorter times (t ≲104) the discreteness of the elementary motion cannot be neglected, whereas for longer times and short chains (N≲100) tube renewal plays an essential role also for the central segment. Due to the very broad crossover behavior, both the diffusion coefficient and the reptation time within the range of our simulation do not reach the asymptotic power laws predicted by reptation theory. We present results for the center-of-mass motion, showing the expected intermediate t1/2 behavior, but again only for very long chains. In addition we show results for the motion of the central segment relative to the center of mass, where in some intermediate range we see the expected increase of the effective power beyond the t1/4 law, before saturation sets in. Analysis and simulations agree on defining a new set of criteria as characteristic for reptation of finite chains.

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