Résumé
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.