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Article overview
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Phonon gap and localization lengths in floppy materials | | Gustavo Düring
; Edan Lerner
; Matthieu Wyart
; | | Date: |
16 Apr 2012 | | Abstract: | Gels of semi-flexible polymers, network glasses made of low valence elements,
softly compressed ellipses and dense suspensions under flow are examples of
floppy materials. These systems present collective motions with almost no
restoring force. We study theoretically and numerically the
frequency-dependence of the response of these materials, and the length scales
that characterize their elasticity. We show that isotropic floppy elastic
networks present a phonon gap for frequencies smaller than a frequency
$omega^*$ governed by coordination, and that the elastic response is localized
on a length scale $l_csim 1/sqrt{omega^*}$ that diverges as the phonon gap
vanishes (with a logarithmic correction in the two dimensional case). $l_c$
also characterizes velocity correlations under shear, whereas another length
scale $l^*sim 1/omega^*$ characterizes the effect of pinning boundaries on
elasticity. We discuss the implications of our findings for suspensions flows,
and the correspondence between floppy materials and amorphous solids near
unjamming, where $l_c$ and $l^*$ have also been identified but where their
roles are not fully understood. | | Source: | arXiv, 1204.3542 | | Services: | Forum | Review | PDF | Favorites | |
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