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research article

Phonon gap and localization lengths in floppy materials

Düring, Gustavo
•
Lerner, Edan
•
Wyart, Matthieu  
2013
Soft Matter

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. © The Royal Society of Chemistry 2013.

  • Details
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Type
research article
DOI
10.1039/C2SM25878A
Author(s)
Düring, Gustavo
Lerner, Edan
Wyart, Matthieu  
Date Issued

2013

Publisher

Royal Society of Chemistry

Published in
Soft Matter
Volume

9

Issue

1

Start page

146

End page

154

Editorial or Peer reviewed

REVIEWED

Written at

OTHER

EPFL units
PCSL  
Available on Infoscience
October 18, 2016
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/130507
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