Phonon gap and localization lengths in floppy materials

Gustavo Düring, Edan Lerner, Matthieu Wyart

    Research output: Contribution to journalArticlepeer-review


    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.

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

    ASJC Scopus subject areas

    • General Chemistry
    • Condensed Matter Physics


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