Dynamics of a Rigid Rod in a Glassy Medium

TL;DR

This study uses simulations to analyze how a rigid rod diffuses in a disordered obstacle environment, revealing scaling laws, a dynamic crossover, and violations of classical diffusion relations.

Contribution

It provides a detailed analysis of translational and rotational diffusion of a rigid rod in a static disordered medium, including new scaling laws and the identification of a dynamic crossover.

Findings

$D_{CM}$ follows kinetic theory predictions with an effective radius.

A dynamic crossover in $D_{R}$ occurs when $L$ is comparable to obstacle spacing.

The Stokes-Einstein-Debye relation is violated for large $L$.

Abstract

We present simulations of the motion of a single rigid rod in a disordered static 2d-array of disk-like obstacles. The rotational, $D_{\rm R}$, and center-of-mass translational, $D_{\rm CM}$, diffusion constants are calculated for a wide range of rod length $L$ and density of obstacles $\rho$. It is found that $D_{\rm CM}$ follows the behavior predicted by kinetic theory for a hard disk with an effective radius $R(L)$. A dynamic crossover is observed in $D_{\rm R}$ for $L$ comparable to the typical distance between neighboring obstacles $d_{\rm nn}$. Using arguments from kinetic theory and reptation, we rationalize the scaling laws, dynamic exponents, and prefactors observed for $D_{\rm R}$. In analogy with the enhanced translational diffusion observed in deeply supercooled liquids, the Stokes-Einstein-Debye relation is violated for $L > 0.6d_{\rm nn}$.