### Abstract

A polymer chain configuration space renormalization group method is developed for application to the polymer diffusion equation for a single continuous polymer chain with excluded volume and unaveraged hydrodynamic interactions. The method builds upon our chain configuration space equilibrium formulation which is based on a coarse graining procedure which utilized small chain contour length loop excluded volume interactions to define the renormalization procedure. This approach is generalized to include small loop hydrodynamic interactions within the renormalization scheme. Our coarse graining treatment is combined with the methods of Kawasaki and Gunton, designed to consider dynamical critical phenomena, to provide the chain configuration space renormalization group theory. Calculations are explicitly presented to order ε = 4 - d, where d is the dimensionality of space. However, we show that the dynamical exponent can be obtained exactly from a consideration of the general renormalization scheme without the use of any ε expansion. Thus, it is demonstrated within the diffusion equation model that z = d with hydrodynamic interactions present. In the free draining limit z = 2 + 1/v where v is the exponent for the molecular weight dependence of the chain radius. In the non-free draining limit, this value of z justifies the equality of the so-called static and hydrodynamic radii exponents within the diffusion equation model.

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

Pages (from-to) | 1009-1015 |

Number of pages | 7 |

Journal | The Journal of Chemical Physics |

Volume | 75 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1981 |

Externally published | Yes |

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### ASJC Scopus subject areas

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

### Cite this

*The Journal of Chemical Physics*,

*75*(2), 1009-1015. https://doi.org/10.1063/1.442064

**Conformation space renormalization of polymers. II. Single chain dynamics based on chain diffusion equation model.** / Oono, Yoshitsugu; Freed, Karl F.

Research output: Contribution to journal › Article

*The Journal of Chemical Physics*, vol. 75, no. 2, pp. 1009-1015. https://doi.org/10.1063/1.442064

}

TY - JOUR

T1 - Conformation space renormalization of polymers. II. Single chain dynamics based on chain diffusion equation model

AU - Oono, Yoshitsugu

AU - Freed, Karl F.

PY - 1981/1/1

Y1 - 1981/1/1

N2 - A polymer chain configuration space renormalization group method is developed for application to the polymer diffusion equation for a single continuous polymer chain with excluded volume and unaveraged hydrodynamic interactions. The method builds upon our chain configuration space equilibrium formulation which is based on a coarse graining procedure which utilized small chain contour length loop excluded volume interactions to define the renormalization procedure. This approach is generalized to include small loop hydrodynamic interactions within the renormalization scheme. Our coarse graining treatment is combined with the methods of Kawasaki and Gunton, designed to consider dynamical critical phenomena, to provide the chain configuration space renormalization group theory. Calculations are explicitly presented to order ε = 4 - d, where d is the dimensionality of space. However, we show that the dynamical exponent can be obtained exactly from a consideration of the general renormalization scheme without the use of any ε expansion. Thus, it is demonstrated within the diffusion equation model that z = d with hydrodynamic interactions present. In the free draining limit z = 2 + 1/v where v is the exponent for the molecular weight dependence of the chain radius. In the non-free draining limit, this value of z justifies the equality of the so-called static and hydrodynamic radii exponents within the diffusion equation model.

AB - A polymer chain configuration space renormalization group method is developed for application to the polymer diffusion equation for a single continuous polymer chain with excluded volume and unaveraged hydrodynamic interactions. The method builds upon our chain configuration space equilibrium formulation which is based on a coarse graining procedure which utilized small chain contour length loop excluded volume interactions to define the renormalization procedure. This approach is generalized to include small loop hydrodynamic interactions within the renormalization scheme. Our coarse graining treatment is combined with the methods of Kawasaki and Gunton, designed to consider dynamical critical phenomena, to provide the chain configuration space renormalization group theory. Calculations are explicitly presented to order ε = 4 - d, where d is the dimensionality of space. However, we show that the dynamical exponent can be obtained exactly from a consideration of the general renormalization scheme without the use of any ε expansion. Thus, it is demonstrated within the diffusion equation model that z = d with hydrodynamic interactions present. In the free draining limit z = 2 + 1/v where v is the exponent for the molecular weight dependence of the chain radius. In the non-free draining limit, this value of z justifies the equality of the so-called static and hydrodynamic radii exponents within the diffusion equation model.

UR - http://www.scopus.com/inward/record.url?scp=36749121266&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36749121266&partnerID=8YFLogxK

U2 - 10.1063/1.442064

DO - 10.1063/1.442064

M3 - Article

AN - SCOPUS:36749121266

VL - 75

SP - 1009

EP - 1015

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 2

ER -