### Abstract

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_{e}^{2}〉 seems to be a constant for N = 192, 256, 384 and 512, where τ and 〈R_{e}^{2}〉 denote the longest relaxation time and the mean square end-to-end distance, respectively.

Original language | English |
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Pages (from-to) | 1824-1827 |

Number of pages | 4 |

Journal | Journal of the Physical Society of Japan |

Volume | 72 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2003 Aug 1 |

### Keywords

- Bond fluctuation model
- Diffusion constant
- Lattice model
- Melt
- Monte Carlo simulations
- Polymer chain
- Reptation
- Self-diffusion

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*Journal of the Physical Society of Japan*,

*72*(8), 1824-1827. https://doi.org/10.1143/JPSJ.72.1824