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

TL;DR

This study uses molecular dynamics simulations to analyze how a linear molecule diffuses and rotates in a 2D obstacle field, revealing scaling laws, crossover points, and deviations from classical diffusion relations.

Contribution

It introduces a scaling analysis of diffusion in a random obstacle medium, identifying crossover phenomena and violations of the Stokes-Einstein-Debye relation.

Findings

Diffusion constants follow a master scaling curve.

Crossover points correspond to obstacle configuration geometries.

Violation of classical diffusion relations occurs at high obstacle densities.

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, $D_{\rm CM}$, and for rotation, $D_{\rm R}$, 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 $D_{\rm R}$ and $D_{\rm CM}$ 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 $D_{\rm CM}$ 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.