### Abstract

Relaxation of a single polymer chain trapped in a periodic array of obstacles in two dimensions is studied by Monte Carlo simulations of the bond fluctuation model, where only the excluded volume interaction is taken into account. Relaxation modes and rates of the polymer chain are estimated by solving a generalized eigenvalue problem for the equilibrium time correlation matrices of the coarse-grained relative positions of segments of the polymer chain. The slowest relaxation rate λ_{1} of the polymer chain of N segments behaves as λ_{1} ∝ N^{-3.1}. The pth slowest relaxation rate λ_{p} with p ≥ 2 shows the p-dependence λ_{p} ∝ p^{2.1} and the N-dependence consistent with λ_{p} ∝ N^{-3.1} for small values of p/N. For each N, the slowest relaxation rate λ_{1} is remarkably smaller than the value extrapolated from the behavior λ_{p} ∝ p^{2.1} for p ≥ 2. The behaviors of slow relaxation modes are similar to those of the Rouse modes. These behaviors of the relaxation rates and modes correspond to those of the slithering snake model with the excluded volume interaction.

Original language | English |
---|---|

Pages (from-to) | 2897-2902 |

Number of pages | 6 |

Journal | Journal of the Physical Society of Japan |

Volume | 70 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2001 Oct |

### Fingerprint

### Keywords

- Bond fluctuation model
- Excluded volume interaction
- Monte Carlo simulations
- Obstacles
- Relaxation modes
- Relaxation rates
- Reptation
- Single polymer chain
- Slithering snake model

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of the Physical Society of Japan*,

*70*(10), 2897-2902. https://doi.org/10.1143/JPSJ.70.2897

**Relaxation of a single polymer chain trapped in an array of obstacles in two dimensions.** / Hagita, Katsumi; Ishizuka, Daisuke; Takano, Hiroshi.

Research output: Contribution to journal › Article

*Journal of the Physical Society of Japan*, vol. 70, no. 10, pp. 2897-2902. https://doi.org/10.1143/JPSJ.70.2897

}

TY - JOUR

T1 - Relaxation of a single polymer chain trapped in an array of obstacles in two dimensions

AU - Hagita, Katsumi

AU - Ishizuka, Daisuke

AU - Takano, Hiroshi

PY - 2001/10

Y1 - 2001/10

N2 - Relaxation of a single polymer chain trapped in a periodic array of obstacles in two dimensions is studied by Monte Carlo simulations of the bond fluctuation model, where only the excluded volume interaction is taken into account. Relaxation modes and rates of the polymer chain are estimated by solving a generalized eigenvalue problem for the equilibrium time correlation matrices of the coarse-grained relative positions of segments of the polymer chain. The slowest relaxation rate λ1 of the polymer chain of N segments behaves as λ1 ∝ N-3.1. The pth slowest relaxation rate λp with p ≥ 2 shows the p-dependence λp ∝ p2.1 and the N-dependence consistent with λp ∝ N-3.1 for small values of p/N. For each N, the slowest relaxation rate λ1 is remarkably smaller than the value extrapolated from the behavior λp ∝ p2.1 for p ≥ 2. The behaviors of slow relaxation modes are similar to those of the Rouse modes. These behaviors of the relaxation rates and modes correspond to those of the slithering snake model with the excluded volume interaction.

AB - Relaxation of a single polymer chain trapped in a periodic array of obstacles in two dimensions is studied by Monte Carlo simulations of the bond fluctuation model, where only the excluded volume interaction is taken into account. Relaxation modes and rates of the polymer chain are estimated by solving a generalized eigenvalue problem for the equilibrium time correlation matrices of the coarse-grained relative positions of segments of the polymer chain. The slowest relaxation rate λ1 of the polymer chain of N segments behaves as λ1 ∝ N-3.1. The pth slowest relaxation rate λp with p ≥ 2 shows the p-dependence λp ∝ p2.1 and the N-dependence consistent with λp ∝ N-3.1 for small values of p/N. For each N, the slowest relaxation rate λ1 is remarkably smaller than the value extrapolated from the behavior λp ∝ p2.1 for p ≥ 2. The behaviors of slow relaxation modes are similar to those of the Rouse modes. These behaviors of the relaxation rates and modes correspond to those of the slithering snake model with the excluded volume interaction.

KW - Bond fluctuation model

KW - Excluded volume interaction

KW - Monte Carlo simulations

KW - Obstacles

KW - Relaxation modes

KW - Relaxation rates

KW - Reptation

KW - Single polymer chain

KW - Slithering snake model

UR - http://www.scopus.com/inward/record.url?scp=0035634811&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035634811&partnerID=8YFLogxK

U2 - 10.1143/JPSJ.70.2897

DO - 10.1143/JPSJ.70.2897

M3 - Article

AN - SCOPUS:0035634811

VL - 70

SP - 2897

EP - 2902

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 10

ER -