### 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 |
---|---|

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 |

### Fingerprint

### 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)

### Cite this

*Journal of the Physical Society of Japan*,

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

**Self-diffusion of a polymer chain in a melt.** / Hagita, Katsumi; Takano, Hiroshi.

Research output: Contribution to journal › Article

*Journal of the Physical Society of Japan*, vol. 72, no. 8, pp. 1824-1827. https://doi.org/10.1143/JPSJ.72.1824

}

TY - JOUR

T1 - Self-diffusion of a polymer chain in a melt

AU - Hagita, Katsumi

AU - Takano, Hiroshi

PY - 2003/8

Y1 - 2003/8

N2 - 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 xd ≃ 2.4. The ratio Dτ/〈Re 2〉 seems to be a constant for N = 192, 256, 384 and 512, where τ and 〈Re 2〉 denote the longest relaxation time and the mean square end-to-end distance, respectively.

AB - 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 xd ≃ 2.4. The ratio Dτ/〈Re 2〉 seems to be a constant for N = 192, 256, 384 and 512, where τ and 〈Re 2〉 denote the longest relaxation time and the mean square end-to-end distance, respectively.

KW - Bond fluctuation model

KW - Diffusion constant

KW - Lattice model

KW - Melt

KW - Monte Carlo simulations

KW - Polymer chain

KW - Reptation

KW - Self-diffusion

UR - http://www.scopus.com/inward/record.url?scp=0141977264&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0141977264&partnerID=8YFLogxK

U2 - 10.1143/JPSJ.72.1824

DO - 10.1143/JPSJ.72.1824

M3 - Article

AN - SCOPUS:0141977264

VL - 72

SP - 1824

EP - 1827

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 8

ER -