### Abstract

Relaxation modes and rates of a single polymer chain confined in a straight tube by repulsive walls are studied by Monte Carlo simulations of the bond fluctuation model, where only the excluded volume interaction is taken into account. The relaxation modes and rates are estimated by solving generalized eigenvalue problems for the equilibrium time correlation matrices C^{∥}_{i,j}(t) = 〈(z_{i}(t) - z_{c}(t))(z_{j}(0) - z_{c}(0))〈_{c} and C^{⊥}_{i.j}(t) = 1/2〈r^{⊥}_{i}(t)·r^{⊥} _{j}(0)〉_{c}, where z_{i} and r^{⊥}_{i} are the components of the position vector of the ith segment parallel and perpendicular to the tube axis, respectively, and z_{c} is the parallel component of the center of mass of the polymer chain. For the parallel component, the behavior of the pth slowest relaxation rate λ^{∥}_{p} of a polymer chain of N segments agrees with the scaling prediction λ^{∥}_{p} ≃ λ_{b}(gp/N)^{2} for gp/N ≪ 1, where Ab and g are the slowest relaxation rate within each blob and the number of segments per blob, respectively. The corresponding relaxation modes show the Rouse-like behavior. For the perpendicular components, the behavior of the pth slowest relaxation rate λ^{⊥}_{p} is consistent with the scaling prediction λ^{⊥}_{p} ≃ Ab for gp/N < 1. The behavior of the corresponding relaxation modes is consistent with the blob picture.

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

Pages (from-to) | 401-407 |

Number of pages | 7 |

Journal | Journal of the Physical Society of Japan |

Volume | 68 |

Issue number | 2 |

Publication status | Published - 1999 Feb |

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### Keywords

- Bond fluctuation model
- Monte Carlo simulations
- Relaxation modes
- Relaxation rates
- Scaling analysis
- Single polymer chain
- Tube

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of the Physical Society of Japan*,

*68*(2), 401-407.

**Relaxation of a polymer chain confined in a tube.** / Hagita, Katsumi; Takano, Hiroshi.

Research output: Contribution to journal › Article

*Journal of the Physical Society of Japan*, vol. 68, no. 2, pp. 401-407.

}

TY - JOUR

T1 - Relaxation of a polymer chain confined in a tube

AU - Hagita, Katsumi

AU - Takano, Hiroshi

PY - 1999/2

Y1 - 1999/2

N2 - Relaxation modes and rates of a single polymer chain confined in a straight tube by repulsive walls are studied by Monte Carlo simulations of the bond fluctuation model, where only the excluded volume interaction is taken into account. The relaxation modes and rates are estimated by solving generalized eigenvalue problems for the equilibrium time correlation matrices C∥i,j(t) = 〈(zi(t) - zc(t))(zj(0) - zc(0))〈c and C⊥i.j(t) = 1/2〈r⊥i(t)·r⊥ j(0)〉c, where zi and r⊥i are the components of the position vector of the ith segment parallel and perpendicular to the tube axis, respectively, and zc is the parallel component of the center of mass of the polymer chain. For the parallel component, the behavior of the pth slowest relaxation rate λ∥p of a polymer chain of N segments agrees with the scaling prediction λ∥p ≃ λb(gp/N)2 for gp/N ≪ 1, where Ab and g are the slowest relaxation rate within each blob and the number of segments per blob, respectively. The corresponding relaxation modes show the Rouse-like behavior. For the perpendicular components, the behavior of the pth slowest relaxation rate λ⊥p is consistent with the scaling prediction λ⊥p ≃ Ab for gp/N < 1. The behavior of the corresponding relaxation modes is consistent with the blob picture.

AB - Relaxation modes and rates of a single polymer chain confined in a straight tube by repulsive walls are studied by Monte Carlo simulations of the bond fluctuation model, where only the excluded volume interaction is taken into account. The relaxation modes and rates are estimated by solving generalized eigenvalue problems for the equilibrium time correlation matrices C∥i,j(t) = 〈(zi(t) - zc(t))(zj(0) - zc(0))〈c and C⊥i.j(t) = 1/2〈r⊥i(t)·r⊥ j(0)〉c, where zi and r⊥i are the components of the position vector of the ith segment parallel and perpendicular to the tube axis, respectively, and zc is the parallel component of the center of mass of the polymer chain. For the parallel component, the behavior of the pth slowest relaxation rate λ∥p of a polymer chain of N segments agrees with the scaling prediction λ∥p ≃ λb(gp/N)2 for gp/N ≪ 1, where Ab and g are the slowest relaxation rate within each blob and the number of segments per blob, respectively. The corresponding relaxation modes show the Rouse-like behavior. For the perpendicular components, the behavior of the pth slowest relaxation rate λ⊥p is consistent with the scaling prediction λ⊥p ≃ Ab for gp/N < 1. The behavior of the corresponding relaxation modes is consistent with the blob picture.

KW - Bond fluctuation model

KW - Monte Carlo simulations

KW - Relaxation modes

KW - Relaxation rates

KW - Scaling analysis

KW - Single polymer chain

KW - Tube

UR - http://www.scopus.com/inward/record.url?scp=0033466925&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033466925&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0033466925

VL - 68

SP - 401

EP - 407

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 2

ER -