Diffusion of single long polymers in fixed and low density matrix of obstacles confined to two dimensions

Diffusion properties of a self-avoiding polymer embedded in regularly distributed obstacles with spacing a=20 and confined in two dimensions is studied numerically using the extended bond fluctuation method which we have developed recently. We have observed for the first time to our knowledge, that the mean square displacement of a center monomer $\phi_{M/2}(t)$ exhibits four dynamical regimes, i.e., $\phi_{M/2}(t) \sim t^{\nu_m}$ with $\nu_m\sim 0.6$, 3/8, 3/4, and 1 from the shortest to longest time regimes. The exponents in the second and third regimes are well described by segmental diffusion in the ``self-avoiding tube''. In the fourth (free diffusion) regime, we have numerically confirmed the relation between the reptation time $\tau_d$ and the number of segments $M, \tau_d\propto M^3$.