Relaxation dynamics of a linear molecule in a random static medium: A scaling analysis

Abstract

We present extensive molecular dynamics simulations of the motion of a single linear rigid molecule in a two-dimensional random array of fixed obstacles. The diffusion constant for the center of mass translation, $D_{\mathrm{CM}}$, and for rotation, $D_{\mathrm{R}}$, are calculated for a wide range of the molecular length, $L$, and the density of obstacles, $\rho$. The obtained results follow a master curve $D{\rho }^{\mu }\sim (L^2\rho {)}^{-\nu }$ with an exponent $\mu =-3/4$ and 1/4 for $D_{\mathrm{R}}$ and $D_{\mathrm{CM}}$ respectively, that can be deduced from simple scaling and kinematic arguments. The non-trivial positive exponent $\nu$ shows an abrupt crossover at $L^2\rho ={\zeta }_1$. For $D_{\mathrm{CM}}$ we find a second crossover at $L^2\rho ={\zeta }_2$. The values of ${\zeta }_1$ and ${\zeta }_2$ correspond to the average minor and major axis of the elliptic holes that characterize the random configuration of the obstacles. A violation of the Stokes-Einstein-Debye relation is observed for $L^2\rho >{\zeta }_1$, in analogy with the phenomenon of enhanced translational diffusion observed in supercooled liquids close to the glass transition temperature.

8 pages, 8 figures. Minor changes. To be published in Journal of Chemical Physics

References in corpus (1)

• Translation-Rotation Coupling in Transient Grating Experiments : Theoretical and Experimental Evidences

Cited by in corpus (4)

• Enhanced Diffusion of a Needle in a Planar Course of Point Obstacles
• Mobile particles in an immobile environment: Molecular Dynamics simulation of a binary Yukawa mixture
• Dynamics of a Rigid Rod in a Glassy Medium
• Three-dimensional Brownian diffusion of rod-like macromolecules in the presence of randomly distributed spherical obstacles: Molecular dynamics simulation