Annealed lattice animal model and Flory theory for the melt of non-concatenated rings: Towards the physics of crumpling

Alexander Y. Grosberg

    Research output: Contribution to journalArticlepeer-review

    Abstract

    A Flory theory is constructed for a long polymer ring in a melt of unknotted and non-concatenated rings. The theory assumes that the ring forms an effective annealed branched object and computes its primitive path. It is shown that the primitive path follows self-avoiding statistics and is characterized by the corresponding Flory exponent of a polymer with excluded volume. Based on that, it is shown that rings in the melt are compact objects with overall size proportional to their length raised to the 1/3 power. Furthermore, the contact probability exponent γcontact is estimated, albeit by a poorly controlled approximation, with the result close to 1.1 consistent with both numerical and experimental data.

    Original languageEnglish (US)
    Pages (from-to)560-565
    Number of pages6
    JournalSoft Matter
    Volume10
    Issue number4
    DOIs
    StatePublished - Jan 28 2014

    ASJC Scopus subject areas

    • Chemistry(all)
    • Condensed Matter Physics

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