Conformation Space Renormalization of Polymers. 4. Equilibrium Properties of the Simple Ring Polymer Using Gell-Mann-Low Type Renormalization Group Theory

M. Lipkin; Y. Oono; Karl F. Freed

doi:10.1021/ma50006a024

Conformation Space Renormalization of Polymers. 4. Equilibrium Properties of the Simple Ring Polymer Using Gell-Mann-Low Type Renormalization Group Theory

M. Lipkin, Y. Oono, Karl F. Freed

Physics

Research output: Contribution to journal › Article › peer-review

Abstract

The method of Oono, Ohta, and Freed is used to derive static properties of a ring polymer above θ the point. This method uses the technique of dimensional regularization as formulated in conformational space where monomers are specified by their positions in space and along the chain. The distribution function for an internal vector of a ring polymer is determined by using the renormalization group analysis with an expansion in d = 4-ε space, d being the spatial dimensionality. The distribution function yields exponents describing the asymptotic, long- and short-range, behavior of polymer rings. These exponents are the same to order e as those for linear chains.

Original language	English (US)
Pages (from-to)	1270-1277
Number of pages	8
Journal	Macromolecules
Volume	14
Issue number	5
DOIs	https://doi.org/10.1021/ma50006a024
State	Published - Sep 1981

ASJC Scopus subject areas

Organic Chemistry
Polymers and Plastics
Inorganic Chemistry
Materials Chemistry

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AB - The method of Oono, Ohta, and Freed is used to derive static properties of a ring polymer above θ the point. This method uses the technique of dimensional regularization as formulated in conformational space where monomers are specified by their positions in space and along the chain. The distribution function for an internal vector of a ring polymer is determined by using the renormalization group analysis with an expansion in d = 4-ε space, d being the spatial dimensionality. The distribution function yields exponents describing the asymptotic, long- and short-range, behavior of polymer rings. These exponents are the same to order e as those for linear chains.

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Conformation Space Renormalization of Polymers. 4. Equilibrium Properties of the Simple Ring Polymer Using Gell-Mann-Low Type Renormalization Group Theory

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