Relaxation of a polymer chain confined in a tube

Relaxation modes and rates of a single polymer chain confined in a straight tube 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 are estimated by solving generalized eigenvalue problems for the equilibrium time correlation matrices C-i,j(parallel to)(t) = [(z(i)(t) - z(c)(t))(z(j)(0) - z(c)(0))](c) and C-i,j(perpendicular to)(t) = 1/2[r(i)(perpendicular to)(t) . r(j)(perpendicular to)(0)](c), where z(i) and r(i)(perpendicular to) are the components of the position vector of the ith segment parallel and perpendicular to the tube axis, respectively, and z(c) is the parallel component of the center of mass of the polymer chain. For the parallel component, the behavior of the pth slowest relaxation rate lambda(p)(parallel to) of a polymer chain of N segments agrees with the scaling prediction lambda(p)(parallel to) similar or equal to lambda(b)(gp/N)(2) for gp/N much less than 1, where lambda(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 components, the behavior of the pth slowest relaxation rate lambda(p)(perpendicular to) consistent with the scaling prediction lambda(p)(perpendicular to) similar or equal to lambda(b) for gp/N < 1. The behavior of the corresponding relaxation modes is consistent with the blob picture.