Reptation, Entropic Trapping, Percolation, and Rouse Dynamics of Polymers in “Random” Environments

Abstract

We study the dynamics of polymers in 2D periodic arrays of obstacles where a fraction $(1\ensuremath{-}c)$ of the obstacles have been removed. As expected, we find Rouse and reptation dynamics for $c\ensuremath{\rightarrow}0$ and $c\ensuremath{\rightarrow}1$, respectively. However, we also find that the diffusion coefficient $D$ decreases when we start removing obstacles due to entropic trapping of the polymer within ``pores.'' These pores begin to form large clusters when $c\ensuremath{\approx}0.80$, and $D$ increases when $c$ is decreased further. Our results clarify the nature of the different regimes for a simple random environment and predict that $D(c)$ can be a nonmonotonic function of $c$.