Relaxation of a polymer chain confined in a tube or a slit

Relaxation modes and rates of a single polymer chain confined in a tube or a slit by repulsive walls are studied by Monte Carlo simulations of the bond fluctuation model, where only the excluded volume interaction is taken into account. The relaxation modes and rates of a polymer chain of N segments in the directions parallel and perpendicular to the walls are estimated by solving generalized eigenvalue problems for the equilibrium time correlation matrices of positions of the segments. For the parallel component, the behavior of the pth slowest relaxation rate λ_p^∥ of a polymer chain of N segments agrees with the scaling prediction λ_p^∥≈λ_b(gp/N)^x for gp/N≪1, where x = 2 for a tube and x = 2.5 for a slit. Here, λ_b and g are the slowest relaxation rate within each blob and the number of segments per blob, respectively. The corresponding relaxation modes show the Rouse-like behavior. For the perpendicular component, the behavior of the pth slowest relaxation rate λ_p^⊥ is consistent with the scaling prediction λ_p^⊥≈λ_b for gp/N<1. The behavior of the corresponding relaxation modes is consistent with the blob picture.