### Abstract

A dimensional regularization approach to the renormalization group treatment of polymer excluded volume is formulated in chain conformation space where monomers are specified by their spatial positions and their positions along the chain and the polymers may be taken to be monodisperse. The method utilizes basic scale invariance considerations. First, it is recognized that long wavelength macroscopic descriptions must be well defined in the limit that the minimum atomic or molecular scale Λ is set to zero. Secondly, the microscopic theory is independent of the conveniently chosen macroscopic scale of length κ. The freedom of choice of κ is exploited along with the assumed renormalizability of the theory to provide the renormalization group equations which directly imply the universal scaling laws for macroscopic properties. The renormalizability of the model implies the existence of the general relations between the basic macroparameters, such as chain length, excluded volume, etc., and their microscopic counterparts in the microscopic model for the system. These macro-micro relations are defined through the condition that macroscopic quantities be well defined for polymer chains for any spatial dimensionality. The method is illustrated by calculating the end vector distribution function for all values of end vectors R. The evaluation of this distribution function currently requires the use of expansions in ε=4-d. In this case our distribution reduces to known limits for R→0 or ∞. Subsequent papers will present calculations of the polymer coherent scattering function, the monomer spatial distribution function, and concentration dependent properties.

Original language | English (US) |
---|---|

Pages (from-to) | 6458-6466 |

Number of pages | 9 |

Journal | The Journal of Chemical Physics |

Volume | 74 |

Issue number | 11 |

DOIs | |

State | Published - Jan 1 1981 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*The Journal of Chemical Physics*,

*74*(11), 6458-6466. https://doi.org/10.1063/1.440984

**Application of dimensional regularization to single chain polymer static properties : Conformational space renormalization of polymers. III.** / Oono, Y.; Ohta, T.; Freed, Karl F.

Research output: Contribution to journal › Article

*The Journal of Chemical Physics*, vol. 74, no. 11, pp. 6458-6466. https://doi.org/10.1063/1.440984

}

TY - JOUR

T1 - Application of dimensional regularization to single chain polymer static properties

T2 - Conformational space renormalization of polymers. III

AU - Oono, Y.

AU - Ohta, T.

AU - Freed, Karl F.

PY - 1981/1/1

Y1 - 1981/1/1

N2 - A dimensional regularization approach to the renormalization group treatment of polymer excluded volume is formulated in chain conformation space where monomers are specified by their spatial positions and their positions along the chain and the polymers may be taken to be monodisperse. The method utilizes basic scale invariance considerations. First, it is recognized that long wavelength macroscopic descriptions must be well defined in the limit that the minimum atomic or molecular scale Λ is set to zero. Secondly, the microscopic theory is independent of the conveniently chosen macroscopic scale of length κ. The freedom of choice of κ is exploited along with the assumed renormalizability of the theory to provide the renormalization group equations which directly imply the universal scaling laws for macroscopic properties. The renormalizability of the model implies the existence of the general relations between the basic macroparameters, such as chain length, excluded volume, etc., and their microscopic counterparts in the microscopic model for the system. These macro-micro relations are defined through the condition that macroscopic quantities be well defined for polymer chains for any spatial dimensionality. The method is illustrated by calculating the end vector distribution function for all values of end vectors R. The evaluation of this distribution function currently requires the use of expansions in ε=4-d. In this case our distribution reduces to known limits for R→0 or ∞. Subsequent papers will present calculations of the polymer coherent scattering function, the monomer spatial distribution function, and concentration dependent properties.

AB - A dimensional regularization approach to the renormalization group treatment of polymer excluded volume is formulated in chain conformation space where monomers are specified by their spatial positions and their positions along the chain and the polymers may be taken to be monodisperse. The method utilizes basic scale invariance considerations. First, it is recognized that long wavelength macroscopic descriptions must be well defined in the limit that the minimum atomic or molecular scale Λ is set to zero. Secondly, the microscopic theory is independent of the conveniently chosen macroscopic scale of length κ. The freedom of choice of κ is exploited along with the assumed renormalizability of the theory to provide the renormalization group equations which directly imply the universal scaling laws for macroscopic properties. The renormalizability of the model implies the existence of the general relations between the basic macroparameters, such as chain length, excluded volume, etc., and their microscopic counterparts in the microscopic model for the system. These macro-micro relations are defined through the condition that macroscopic quantities be well defined for polymer chains for any spatial dimensionality. The method is illustrated by calculating the end vector distribution function for all values of end vectors R. The evaluation of this distribution function currently requires the use of expansions in ε=4-d. In this case our distribution reduces to known limits for R→0 or ∞. Subsequent papers will present calculations of the polymer coherent scattering function, the monomer spatial distribution function, and concentration dependent properties.

UR - http://www.scopus.com/inward/record.url?scp=36749106457&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36749106457&partnerID=8YFLogxK

U2 - 10.1063/1.440984

DO - 10.1063/1.440984

M3 - Article

AN - SCOPUS:36749106457

VL - 74

SP - 6458

EP - 6466

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 11

ER -