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

Abstract

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 10⁷Monte Carlo steps. For N≥ 160, for the central segment we find clear t ^1/4behavior as an intermediate asymptote. The expected t ^1/2range is not yet developed. For the end segment also the t ^l/4behavior 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 t ^1/2behavior, 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 t ^1/4law, before saturation sets in. Analysis and simulations agree on defining a new set of criteria as characteristic for reptation of finite chains.