Dynamical Properties of the Slithering Snake Algorithm: A numerical test of the activated reptation hypothesis

TL;DR

This study uses kinetic Monte Carlo simulations to examine the dynamics of reptating polymers, revealing deviations from classical reptation theory at high densities due to chain end effects and anomalous diffusion.

Contribution

It provides a numerical test of the activated reptation hypothesis, showing how chain end density influences polymer relaxation times and subdiffusive behavior.

Findings

Relaxation times increase faster than classical predictions at high densities.

Chain end density enables polymers to escape local cages, affecting dynamics.

Subdiffusive regime caused by slow chain escape from correlation holes.

Abstract

The correlations in the motion of reptating polymers in their melt are investigated by means of kinetic Monte Carlo simulations of the three dimensional slithering snake version of the bond-fluctuation model. Surprisingly, the slithering snake dynamics becomes inconsistent with classical reptation predictions at high chain overlap (either chain length $N$ or volume fraction $\phi$) where the relaxation times increase much faster than expected. This is due to the anomalous curvilinear diffusion in a finite time window whose upper bound $\tau_+$ is set by the chain end density $\phi/N$. Density fluctuations created by passing chain ends allow a reference polymer to break out of the local cage of immobile obstacles created by neighboring chains. The dynamics of dense solutions of snakes at $t \ll \tau_+$ is identical to that of a benchmark system where all but one chain are frozen. We demonstrate that it is the slow creeping of a chain out of its correlation hole which causes the subdiffusive dynamical regime. Our results are in good qualitative agreement with the activated reptation scheme proposed recently by Semenov and Rubinstein [Eur. Phys. J. B, {\bf 1} (1998) 87]. Additionally, we briefly comment on the relevance of local relaxation pathways within a slithering snake scheme. Our preliminary results suggest that a judicious choice of the ratio of local to slithering snake moves is crucial to equilibrate a melt of long chains efficiently.