Relaxation of a single polymer chain trapped in an array of obstacles in two dimensions

Relaxation of a single polymer chain trapped in a periodic array of obstacles in two dimensions is studied by Monte Carlo simulations of the bond fluctuation model, where only the excluded volume interaction is taken into account. Relaxation modes and rates of the polymer chain are estimated by solving a generalized eigenvalue problem for the equilibrium time correlation matrices of the coarse-grained relative positions of segments of the polymer chain. The slowest relaxation rate λ₁ of the polymer chain of N segments behaves as λ₁ ∝ N^-3.1. The pth slowest relaxation rate λ_p with p ≥ 2 shows the p-dependence λ_p ∝ p^2.1 and the N-dependence consistent with λ_p ∝ N^-3.1 for small values of p/N. For each N, the slowest relaxation rate λ₁ is remarkably smaller than the value extrapolated from the behavior λ_p ∝ p^2.1 for p ≥ 2. The behaviors of slow relaxation modes are similar to those of the Rouse modes. These behaviors of the relaxation rates and modes correspond to those of the slithering snake model with the excluded volume interaction.