Self-Diffusion of a Polymer Chain in a Melt

Self-diffusion of a polymer chain in a melt is 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 × 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 the times larger than the longest relaxation time. From the data for $N = 256$, 384 and 512, the apparent exponent xd, which describes the apparent power law dependence of D on N as D ∝ N^- xd, is estimated as xd 2.4. The ratio D τ / < Rₑ² > seems to be a constant for $N = 192, 256, 384$ and 512, where τ and $ $ denote the longest relaxation time and the mean square end-to-end distance, respectively.