Dynamics of a Rigid Rod in a Glassy Medium

Details Dynamics of a Rigid Rod in a Glassy Medium Dynamics of a Rigid Rod in a Glassy Medium

2003-10-20

arxiv.org/abs/cond-mat/0310447v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

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

Scientific paper

10.1209/epl/i2004-10172-y

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 $L > 0.6d_{\rm nn}$.

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