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 j (0) >/ 3 , where R i ( t ) denotes the position of the i th segment relative to the center of mass of the polymer chain. For a chain of N segments with the excluded volume interaction, the contribution \(g̃i,p\) of the p th slowest mode to R i shows the i -dependence \(g̃i,p ∝ cos [(i-1/2)p π / N]\), which is the same as that of the Rouse model. The behavior of the relaxation rate λ p of the p th slowest mode is in good agreement with the theoretical prediction λ p ∼( p / N ) 2ν+ 1 , where ν≃0.588 is the exponent for the swelling of a polymer chain in good solvent.