Self-Diffusion of a Polymer Chain in a Melt

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  • Hagita Katsumi
    Department of Physics, Faculty of Science and Technology, Keio University
  • Takano Hiroshi
    Department of Physics, Faculty of Science and Technology, Keio University

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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\\simeq0.5 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 xd, which describes the apparent power law dependence of D on N as D∝N−xd, is estimated to be xd\\simeq2.4. The ratio Dτ⁄⟨Re2⟩ seems to be a constant for N=192,256,384 and 512, where τ and ⟨Re2⟩ denote the longest relaxation time and the mean square end-to-end distance, respectively.

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