Relaxation modes and rates of a single polymer chain in a periodic array of obstacles

The relaxation modes and rates of a single polymer chain in the two-dimensional space with periodically placed obstacles are studied by Monte Carlo simulations. The bond fluctuation model is used as a model of a polymer chain. The excluded volume interactions between segments are taken into account. Each segment of the polymer chain occupies a square of width 2a, where a is the lattice constant of the square lattice used in the bond fluctuation model. The obstacles are squares of width 8a and form a square lattice with the lattice constant 16a. From the lattice model of reptation, it is expected that a polymer chain in the periodic array of obstacles shows the reptation behavior. The behavior of the pth slowest relaxation rate of a polymer chain of N segments is found to agree with the prediction λ_p α p²/N₃. The behaviors of the diffusion constant of the center of mass and the radius of gyration are also consistent with the relation D_G/λ_p=1 α R²_g, which is expected from the reptation theory.