### Abstract

Relaxation and self-diffusion of a polymer chain in a melt are discussed on the basis of the results of our recent Monte Carlo simulations of the bond fluctuation model, where only the excluded volume interaction is considered. Polymer chains are located on an L × L × L simple cubic lattice under periodic boundary conditions. Each chain consists of N segments, each of which 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 examined, where L- 128 for N ≤ 256 and L= 192 for N ≥ 384. The longest relaxation time τ is estimated by solving generalized eigenvalue problems for the equilibrium time correlation matrices of the positions of segments of a polymer chain. The self-diffusion constant D is estimated from the mean square displacements of the center of mass of a single polymer chain at the times larger than τ. From the data for N = 256, 384 and 512, the apparent exponents x _{r} and x_{d}, which describe the power law dependences of τ and D on N as τ ∝ N^{xr} and D ∝ N^{xd}, are estimated to be x_{r} ≈ 3.5 and x_{d} ≈ 2.4, respectively. For N = 192,256, 384 and 512, Dτ/〈R_{e} ^{2}〉 appears to be a constant, where 〈R_{e} ^{2}〉 denotes the mean square end-to-end distance of a polymer chain.

Original language | English |
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Title of host publication | Slow Dynamics in Complex Systems |

Subtitle of host publication | 3rd International Symposium on Slow Dynamics in Complex Systems |

Publisher | American Institute of Physics Inc. |

Pages | 279-280 |

Number of pages | 2 |

Volume | 708 |

ISBN (Electronic) | 0735401837 |

DOIs | |

Publication status | Published - 2004 Apr 30 |

Event | 3rd International Symposium on Slow Dynamics in Complex Systems - Sendai, Japan Duration: 2003 Nov 3 → 2003 Nov 8 |

### Other

Other | 3rd International Symposium on Slow Dynamics in Complex Systems |
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Country | Japan |

City | Sendai |

Period | 03/11/3 → 03/11/8 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Slow Dynamics in Complex Systems: 3rd International Symposium on Slow Dynamics in Complex Systems*(Vol. 708, pp. 279-280). American Institute of Physics Inc.. https://doi.org/10.1063/1.1764143

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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Slow Dynamics in Complex Systems: 3rd International Symposium on Slow Dynamics in Complex Systems.*vol. 708, American Institute of Physics Inc., pp. 279-280, 3rd International Symposium on Slow Dynamics in Complex Systems, Sendai, Japan, 03/11/3. https://doi.org/10.1063/1.1764143

}

TY - GEN

T1 - Relaxation and self-diffusion of a polymer chain in a melt

AU - Hagita, Katsumi

AU - Takano, Hiroshi

PY - 2004/4/30

Y1 - 2004/4/30

N2 - Relaxation and self-diffusion of a polymer chain in a melt are discussed on the basis of the results of our recent Monte Carlo simulations of the bond fluctuation model, where only the excluded volume interaction is considered. Polymer chains are located on an L × L × L simple cubic lattice under periodic boundary conditions. Each chain consists of N segments, each of which 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 examined, where L- 128 for N ≤ 256 and L= 192 for N ≥ 384. The longest relaxation time τ is estimated by solving generalized eigenvalue problems for the equilibrium time correlation matrices of the positions of segments of a polymer chain. The self-diffusion constant D is estimated from the mean square displacements of the center of mass of a single polymer chain at the times larger than τ. From the data for N = 256, 384 and 512, the apparent exponents x r and xd, which describe the power law dependences of τ and D on N as τ ∝ Nxr and D ∝ Nxd, are estimated to be xr ≈ 3.5 and xd ≈ 2.4, respectively. For N = 192,256, 384 and 512, Dτ/〈Re 2〉 appears to be a constant, where 〈Re 2〉 denotes the mean square end-to-end distance of a polymer chain.

AB - Relaxation and self-diffusion of a polymer chain in a melt are discussed on the basis of the results of our recent Monte Carlo simulations of the bond fluctuation model, where only the excluded volume interaction is considered. Polymer chains are located on an L × L × L simple cubic lattice under periodic boundary conditions. Each chain consists of N segments, each of which 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 examined, where L- 128 for N ≤ 256 and L= 192 for N ≥ 384. The longest relaxation time τ is estimated by solving generalized eigenvalue problems for the equilibrium time correlation matrices of the positions of segments of a polymer chain. The self-diffusion constant D is estimated from the mean square displacements of the center of mass of a single polymer chain at the times larger than τ. From the data for N = 256, 384 and 512, the apparent exponents x r and xd, which describe the power law dependences of τ and D on N as τ ∝ Nxr and D ∝ Nxd, are estimated to be xr ≈ 3.5 and xd ≈ 2.4, respectively. For N = 192,256, 384 and 512, Dτ/〈Re 2〉 appears to be a constant, where 〈Re 2〉 denotes the mean square end-to-end distance of a polymer chain.

UR - http://www.scopus.com/inward/record.url?scp=85048162832&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85048162832&partnerID=8YFLogxK

U2 - 10.1063/1.1764143

DO - 10.1063/1.1764143

M3 - Conference contribution

AN - SCOPUS:85048162832

VL - 708

SP - 279

EP - 280

BT - Slow Dynamics in Complex Systems

PB - American Institute of Physics Inc.

ER -