On the Divergence of the Perturbation Series for the Excluded-Volume Problem in Polymers. II. Collapse of a Single Chain in Poor Solvents

Yoshitsugu Oono

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Abstract

For a lattice polymer on the cubic lattice in three dimensional space, it is proved that a single polymer chain is contained in a small volume with probability 1 for negative real z, the measure of the strength of the intrachain interaction, when the polymer length becomes infinite with z being kept finite. The result suggests that the radii of convergence of the perturbation series so far obtained for a chain of finite length N are of order N-1/2.

Original languageEnglish (US)
Pages (from-to)787-793
Number of pages7
JournalJournal of the Physical Society of Japan
Volume41
Issue number3
DOIs
StatePublished - Jan 1 1976

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divergence
perturbation
polymers
cubic lattices
radii
interactions

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

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abstract = "For a lattice polymer on the cubic lattice in three dimensional space, it is proved that a single polymer chain is contained in a small volume with probability 1 for negative real z, the measure of the strength of the intrachain interaction, when the polymer length becomes infinite with z being kept finite. The result suggests that the radii of convergence of the perturbation series so far obtained for a chain of finite length N are of order N-1/2.",
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N2 - For a lattice polymer on the cubic lattice in three dimensional space, it is proved that a single polymer chain is contained in a small volume with probability 1 for negative real z, the measure of the strength of the intrachain interaction, when the polymer length becomes infinite with z being kept finite. The result suggests that the radii of convergence of the perturbation series so far obtained for a chain of finite length N are of order N-1/2.

AB - For a lattice polymer on the cubic lattice in three dimensional space, it is proved that a single polymer chain is contained in a small volume with probability 1 for negative real z, the measure of the strength of the intrachain interaction, when the polymer length becomes infinite with z being kept finite. The result suggests that the radii of convergence of the perturbation series so far obtained for a chain of finite length N are of order N-1/2.

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