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

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 |

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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

**Relaxation Mode Analysis of a Single Polymer Chain in a Melt.** / Hagita, Katsumi; Takano, Hiroshi.

Research output: Contribution to journal › Article

*Journal of the Physical Society of Japan*, vol. 71, no. 3, pp. 673-676. https://doi.org/10.1143/JPSJ.71.673

}

TY - JOUR

T1 - Relaxation Mode Analysis of a Single Polymer Chain in a Melt

AU - Hagita, Katsumi

AU - Takano, Hiroshi

PY - 2002/3

Y1 - 2002/3

N2 - 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 Ci,j(t) = 1/3 〈R̄i(t) · R̄j(0)〉 of the coarse-grained relative positions R̄i of segments of a polymer chain defined by R̄ i = 1/n ∑k=1n R(i-1)n+k, where Rk 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 λ1 as λ1 ∝ 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 λp for a fixed value of N is consistent with the prediction of the reptation theory λp ∝ p2. The first and second slowest relaxation modes show the Rouse-like behavior.

AB - 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 Ci,j(t) = 1/3 〈R̄i(t) · R̄j(0)〉 of the coarse-grained relative positions R̄i of segments of a polymer chain defined by R̄ i = 1/n ∑k=1n R(i-1)n+k, where Rk 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 λ1 as λ1 ∝ 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 λp for a fixed value of N is consistent with the prediction of the reptation theory λp ∝ p2. The first and second slowest relaxation modes show the Rouse-like behavior.

KW - Bond fluctuation model

KW - Lattice model

KW - Melt

KW - Monte Carlo simulations

KW - Polymer chain

KW - Relaxation modes

KW - Relaxation rates

KW - Reptation

UR - http://www.scopus.com/inward/record.url?scp=0036246004&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036246004&partnerID=8YFLogxK

U2 - 10.1143/JPSJ.71.673

DO - 10.1143/JPSJ.71.673

M3 - Article

AN - SCOPUS:0036246004

VL - 71

SP - 673

EP - 676

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 3

ER -