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Issue 1, 2013
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Phonon gap and localization lengths in floppy materials

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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 Image ID:c2sm25878a-t5.gif 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.

Graphical abstract: Phonon gap and localization lengths in floppy materials

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Publication details

The article was received on 16 Apr 2012, accepted on 14 Sep 2012 and first published on 15 Oct 2012


Article type: Paper
DOI: 10.1039/C2SM25878A
Citation: Soft Matter, 2013,9, 146-154

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    Phonon gap and localization lengths in floppy materials

    G. Düring, E. Lerner and M. Wyart, Soft Matter, 2013, 9, 146
    DOI: 10.1039/C2SM25878A

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