Diffusion in the two-dimensional necklace model for reptation

An extension of a recently introduced one-dimensional model, the necklace model, is used to study the reptation of a chain of N particles in a two-dimensional square lattice. The mobilities of end and middle particles of a chain are governed by three free parameters. This new model mimics the behavior of a long linear and flexible polymer in a gel. Noninteracting and self-avoiding chains are considered. For both cases, analytical approximations for the diffusion coefficient of the center of mass of the chain, for all values of N, are proposed. The validity of these approximations for different values of the free parameters is verified by means of Monte Carlo simulations. Extensions to higher dimensions are also discussed.