Monte Carlo study of relaxation modes of a single polymer chain

The relaxation modes and rates of a single polymer chain are studied by Monte Carlo simulations of the bond fluctuation model. On the basis of the method proposed by Takano and Miyashita [J. Phys. Sec. Jpn. 64 (1995) 3688], the approximate relaxation modes and rates are obtained by solving a generalized eigenvalue problem for the correlation matrices C-i,C-j(t) = [R-i(t) . R-j(0)]/3, where R-i(t) denotes the position of the ith segment relative to the center of mass of the polymer chain. For a chain of N segments with the excluded volume interaction. the contribution (g) over tilde(i,p) Of the pth slowest mode to R-i shows the i-dependence (g) over tilde(i,p) CC cos[(i - 1/2)p pi/N], which, which is the same as that of the Rouse model. The behavior of the relaxation rate lambda(p) of the pth slowest mode is in good agreement with the theoretical prediction lambda(p) similar to (p/N)(2 nu+1), where nu similar to 0.588 is the exponent for the swelling of a polymer chain in good solvent.