### Abstract

Relaxation modes and rates of a polymer chain in a melt are 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 relaxation modes and rates are estimated by solving generalized eigenvalue problems for the equilibrium time correlation matrices C_{i,j}(t) = 1/3 〈R̄_{i}(t) · R̄_{j}(0)〉 of the coarse-grained relative positions R̄_{i} of segments of a polymer chain defined by R̄ _{i} = 1/n ∑_{k=1}^{n} R_{(i-1)n+k}, where R_{k} denotes the position of the kth segment relative to the center of mass of the polymer chain. The apparent exponent z which describes the N-dependence of the slowest relaxation rate λ_{1} as λ_{1} ∝ N^{-z} increases beyond three as N increases. From the data for N = 256, 384 and 512, the apparent exponent is estimated to be z ≃ 3.5. The behavior of the pth slowest relaxation rate λ_{p} for a fixed value of N is consistent with the prediction of the reptation theory λ_{p} ∝ p^{2}. The first and second slowest relaxation modes show the Rouse-like behavior.

Original language | English |
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Pages (from-to) | 673-676 |

Number of pages | 4 |

Journal | Journal of the Physical Society of Japan |

Volume | 71 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2002 Mar 1 |

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### Keywords

- Bond fluctuation model
- Lattice model
- Melt
- Monte Carlo simulations
- Polymer chain
- Relaxation modes
- Relaxation rates
- Reptation

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of the Physical Society of Japan*,

*71*(3), 673-676. https://doi.org/10.1143/JPSJ.71.673