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. Soc. Jpn. 64 (1995) 3688], the approximate relaxation modes and rates are obtained by solving a generalized eigenvalue problem for the correlation matrices C_i,_j(t) = <R_i(t) · R_i(t)>/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 g̃_i,p of the pth slowest mode to R_i shows the i-dependence g̃_i,p α cos[(i - 1/2)pπ/N], which is the same as that of the Rouse model. The behavior of the relaxation rate λ_p of the pth slowest mode is in good agreement with the theoretical prediction λ_p ∼ (P/N)^2v+1, where v ≃ 0.588 is the exponent for the swelling of a polymer chain in good solvent.