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

TL;DR

This paper presents simulation data on polymer chain motion in a lattice obstacle model, confirming theoretical predictions of reptation behavior and highlighting finite chain effects and crossover phenomena.

Contribution

It provides detailed simulation results for various chain lengths, validating and extending analytical reptation models with new criteria for finite chain reptation behavior.

Findings

Clear t^{1/4} behavior for central segments in long chains

Discreteness effects dominate at short times

Tube renewal influences short chains and longer times

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 $10^{7}$ Monte Carlo steps. For $N \geq 160$ we for the central segment find clear $t^{1/4}$-behavior as an intermediate asymptote. The also expected $t^{1/2}$-range is not yet developed. For the end segment also the $t^{1/4}$-behavior is not reached. All these data compare well to our recent analytical evaluation of the reptation model, which shows that for shorter times $(t \alt 10^{4})$ the discreteness of the elementary motion cannot be neglected, whereas for longer times and short chains $(N \alt 100)$ 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 $t^{1/2}$-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 $t^{1/4}$-law, before saturation sets in. Analysis and simulations agree on defining a new set of criteria as characteristic for reptation of finite chains.