Journal
SOFT MATTER
Volume 9, Issue 1, Pages 146-154Publisher
ROYAL SOC CHEMISTRY
DOI: 10.1039/c2sm25878a
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Funding
- Sloan Fellowship
- NSF [DMR-1105387]
- Petroleum Research Fund [52031-DNI9]
- MRSEC Program of the National Science Foundation [DMR-0820341]
- Division Of Materials Research
- Direct For Mathematical & Physical Scien [1105387] Funding Source: National Science Foundation
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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 omega* governed by coordination, and that the elastic response is characterized, and in some cases localized, on a length scale l(c) similar to 1/root 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* similar to 1/omega* 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 l(c) and l* have also been identified but where their roles are not fully understood.
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