Phonon gap and localization lengths in floppy materials

Gustavo Düring, Edan Lerner, Matthieu Wyart

    Research output: Contribution to journalArticle

    Abstract

    Gels of semi-flexible polymers, network glasses made of low valence elements, softly compressed ellipsoid particles and dense suspensions under flow are examples of floppy materials. These systems present collective motions with almost no restoring force. To study theoretically and numerically the frequency-dependence of the response of these materials and the length scales that characterize their elasticity, we use a model of isotropic floppy elastic networks. We show that such networks present a phonon gap for frequencies smaller than a frequency ω* governed by coordination, and that the elastic response is characterized, and in some cases localized, on a length scale that diverges as the phonon gap vanishes (with a logarithmic correction in the two dimensional case). lc also characterizes velocity correlations under shear, whereas another length scale l * ∼ 1/ω* controls the effect of pinning boundaries on elasticity. We discuss the implications of our findings for suspension flows, and the correspondence between floppy materials and amorphous solids near unjamming, where lc and l* have also been identified but where their roles are not fully understood. This journal is

    Original languageEnglish (US)
    Pages (from-to)146-154
    Number of pages9
    JournalSoft Matter
    Volume9
    Issue number1
    DOIs
    StatePublished - Jan 7 2013

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    Elasticity
    Suspensions
    elastic properties
    ellipsoids
    Polymers
    Gels
    gels
    shear
    valence
    Glass
    glass
    polymers

    ASJC Scopus subject areas

    • Chemistry(all)
    • Condensed Matter Physics

    Cite this

    Phonon gap and localization lengths in floppy materials. / Düring, Gustavo; Lerner, Edan; Wyart, Matthieu.

    In: Soft Matter, Vol. 9, No. 1, 07.01.2013, p. 146-154.

    Research output: Contribution to journalArticle

    Düring, G, Lerner, E & Wyart, M 2013, 'Phonon gap and localization lengths in floppy materials', Soft Matter, vol. 9, no. 1, pp. 146-154. https://doi.org/10.1039/c2sm25878a
    Düring, Gustavo ; Lerner, Edan ; Wyart, Matthieu. / Phonon gap and localization lengths in floppy materials. In: Soft Matter. 2013 ; Vol. 9, No. 1. pp. 146-154.
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