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

We present extensive molecular dynamics simulations of the motion of a single linear rigid molecule in a two-dimensional random array of fixed overlapping disklike obstacles. The diffusion constants for the center of mass translation, D(CM), and for rotation, D(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 Drho(micro) approximately (L(2)rho)(-nu) with an exponent micro=-3/4 and 1/4 for D(R) and D(CM), respectively, that can be deduced from simple scaling and kinematic arguments. The nontrivial positive exponent nu shows an abrupt crossover at L(2)rho=zeta(1). For D(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.