Dynamics of a Rigid Rod in a Glassy Medium

Abstract

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

8 pages, 4 figures. Major changes. To be published in Europhysics Letters