### Abstract

Two alternative approaches are presented for evaluating the rotational diffusion constant D_{r} of entangled rodlike polymers in a semidilute solution. One is a quantitative refinement of the Doi-Edwards tube model, which gave for the first time a qualitative expression of D_{r}. To evaluate the mean square of a step angular displacement of the rodlike molecule, we use a computer simulation for Poisson line processes, while the mean lifetime of the tube is calculated by use of the first exit time of a stochastic process. The result is in good agreement with experimental data so far obtained. The other approach is a new Green function formulation on the dynamics of entangled rods; we regard the obstructions by neighbouring rods as a sequence of perturbation elements exerted on the free diffusion of the test rod. Incorporating the effects of the sequential perturbation one by one, we obtain an expression of D_{r} for rods in solutions in a wide range of concentrations from dilute to semidilute. In the semidilute region, this reduces to the result of the tube model.

Original language | English (US) |
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Title of host publication | Springer Series in Chemical Physics |

Publisher | Publ by Springer-Verlag New York |

Pages | 132-140 |

Number of pages | 9 |

Edition | 51 |

ISBN (Print) | 3540508295 |

State | Published - 1989 |

Event | Proceedings of the 11th Tanaguchi International Symposium - Hakone, Jpn Duration: Nov 7 1988 → Nov 12 1988 |

### Other

Other | Proceedings of the 11th Tanaguchi International Symposium |
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City | Hakone, Jpn |

Period | 11/7/88 → 11/12/88 |

### Fingerprint

### ASJC Scopus subject areas

- Physical and Theoretical Chemistry

### Cite this

*Springer Series in Chemical Physics*(51 ed., pp. 132-140). Publ by Springer-Verlag New York.

**Molecular theory of the entanglement effect of rodlike polymers. Two alternative approaches.** / Teraoka, Iwao; Hayakawa, R.

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

*Springer Series in Chemical Physics.*51 edn, Publ by Springer-Verlag New York, pp. 132-140, Proceedings of the 11th Tanaguchi International Symposium, Hakone, Jpn, 11/7/88.

}

TY - CHAP

T1 - Molecular theory of the entanglement effect of rodlike polymers. Two alternative approaches

AU - Teraoka, Iwao

AU - Hayakawa, R.

PY - 1989

Y1 - 1989

N2 - Two alternative approaches are presented for evaluating the rotational diffusion constant Dr of entangled rodlike polymers in a semidilute solution. One is a quantitative refinement of the Doi-Edwards tube model, which gave for the first time a qualitative expression of Dr. To evaluate the mean square of a step angular displacement of the rodlike molecule, we use a computer simulation for Poisson line processes, while the mean lifetime of the tube is calculated by use of the first exit time of a stochastic process. The result is in good agreement with experimental data so far obtained. The other approach is a new Green function formulation on the dynamics of entangled rods; we regard the obstructions by neighbouring rods as a sequence of perturbation elements exerted on the free diffusion of the test rod. Incorporating the effects of the sequential perturbation one by one, we obtain an expression of Dr for rods in solutions in a wide range of concentrations from dilute to semidilute. In the semidilute region, this reduces to the result of the tube model.

AB - Two alternative approaches are presented for evaluating the rotational diffusion constant Dr of entangled rodlike polymers in a semidilute solution. One is a quantitative refinement of the Doi-Edwards tube model, which gave for the first time a qualitative expression of Dr. To evaluate the mean square of a step angular displacement of the rodlike molecule, we use a computer simulation for Poisson line processes, while the mean lifetime of the tube is calculated by use of the first exit time of a stochastic process. The result is in good agreement with experimental data so far obtained. The other approach is a new Green function formulation on the dynamics of entangled rods; we regard the obstructions by neighbouring rods as a sequence of perturbation elements exerted on the free diffusion of the test rod. Incorporating the effects of the sequential perturbation one by one, we obtain an expression of Dr for rods in solutions in a wide range of concentrations from dilute to semidilute. In the semidilute region, this reduces to the result of the tube model.

UR - http://www.scopus.com/inward/record.url?scp=0024867563&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0024867563&partnerID=8YFLogxK

M3 - Chapter

SN - 3540508295

SP - 132

EP - 140

BT - Springer Series in Chemical Physics

PB - Publ by Springer-Verlag New York

ER -