Self-diffusion of a polymer chain in a melt

Self-diffusion of a polymer chain in a melt is studied by Monte Carlo simulations using 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 × L × L simple cubic lattice under periodic boundary conditions, where each segment occupies 2 × 2 × 2 unit cells. The results for N = 32, 48, 64, 96, 128, 192, 256, 384 and 512 at the volume fraction φ ≃ 0.5 are reported, where L = 128 for N ≤ 256 and L = 192 for N ≥ 384. The N-dependence of the self-diffusion constant D is examined. Here, D is estimated from the mean square displacements of the center of mass of a single polymer chain at times longer than the longest relaxation time. From the data for N = 256, 384 and 512, the apparent exponent x _d, which describes the apparent power law dependence of D on N as D ∝ N^-xd, is estimated to be x_d ≃ 2.4. The ratio Dτ/〈R_e²〉 seems to be a constant for N = 192, 256, 384 and 512, where τ and 〈R_e²〉 denote the longest relaxation time and the mean square end-to-end distance, respectively.