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 distr ibuted obstacles with spacing a = 20 and confined in two dimensions is stud ied numerically using the extended bond fluctuation method which we have de veloped recently. We have observed for the first time to our knowledge, tha t the mean square displacement of a center monomer phi(M/2) (t) exhibits fo ur dynamical regimes, i.e., phi(M/2) (t) similar to t(nu m) with nu(m) simi lar to 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 d iffusion in the "self-avoiding tube.'' In the fourth (free diffusion) regim e, we have numerically confirmed the relation between the reptation time ta u(d) and the number of segments M, tau(d)proportional to M-3. (C) 1999 Amer ican Institute of Physics. [S0021-9606(99)51442-6].