Relaxation mode analysis of a single polymer chain in a melt

Relaxation modes and rates of a polymer chain in a melt are studied by Monte Carlo simulations of the bond fluctuation model, where only the excluded volume interaction is taken into account. Polymer chains, each of which consists of N segments, are located on an L x L x L simple cubic lattice under periodic boundary conditions, where each segment occupies 2 x 2 x 2 unit cells. The results for N = 32, 48, 64, 96, 128, 192, 256, 384 and 512 at the volume fraction phi similar or equal to 0.5 are reported, where L = 128 for N less than or equal to 256 and L = 192 for N greater than or equal to 384. The relaxation modes and rates are estimated by solving generalized eigenvalue problems for the equilibrium time correlation matrices C-i,C-j(t)= 1/3 <(R) over bar (i)(t) (.) (R) over bar (j)(0)> of the coarsegrained relative positions (R) over bar (i) of segments of a polymer chain defined by (R) over bar (i) = 1/n Sigma(k=1) (n) R(i-1)n+k, where R-k denotes the position of the kth segment relative to the center of mass of the polymer chain. The apparent exponent z which describes the N-dependence of the slowest relaxation rate lambda(1) as lambda(1) proportional to N-z increases beyond three as N increases. From the data for N = 256, 384 and 512, the apparent exponent is estimated to be z similar or equal to 3.5. The behavior of the pth slowest relaxation rate lambda(p) for a fixed value of N is consistent with the prediction of the reptation theory lambda(p) proportional to p(2). The first and second slowest relaxation modes show the Rouse-like behavior.