Disordered surface vibrations in jammed sphere packings

Sussman, Daniel M.; Goodrich, Carl P.; Liu, Andrea J.; Nagel, Sidney R.

doi:10.1039/c4sm02905d

Disordered surface vibrations in jammed sphere packings

Journal Article · Wed Feb 11 00:00:00 EST 2015 · Soft Matter

DOI:https://doi.org/10.1039/c4sm02905d· OSTI ID:1596345

Sussman, Daniel M. ^[1]; Goodrich, Carl P. ^[2]; Liu, Andrea J. ^[2]; Nagel, Sidney R. ^[3]

Univ. of Pennsylvania, Philadelphia, PA (United States); The University of Chicago
Univ. of Pennsylvania, Philadelphia, PA (United States)
Univ. of Chicago, IL (United States)

We study the vibrational properties near a free surface of disordered spring networks derived from jammed sphere packings. In bulk systems, without surfaces, it is well understood that such systems ω* frequency is controlled by ΔZ = $$\langle$$Z$$\rangle$$ - 2d, the difference between the average coordination of the spheres and twice the spatial dimension, d, of the system, which vanishes at the jamming transition. In the presence of a free surface we find that there is a density of disordered vibrational modes associated with the surface that extends far below ω . The total number of these low-frequency surface modes is controlled by ΔZ, and the profile of their decay into the bulk has two characteristic length scales, which diverge as ΔZ^-1/2 and ΔZ^-1 as the jamming transition is approached.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Chicago, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: FG02-03ER46088

OSTI ID:: 1596345

Journal Information:: Soft Matter, Journal Name: Soft Matter Journal Issue: 14 Vol. 11; ISSN SMOABF; ISSN 1744-683X

Publisher:: Royal Society of ChemistryCopyright Statement

Country of Publication:: United States

Language:: English

References (27)

Bulk and surface floppy modes Thorpe, M. F. Journal of Non-Crystalline Solids, Vol. 182, Issue 1-2 https://doi.org/10.1016/0022-3093(94)00545-1	journal	March 1995
Amorphous solids: their structure, lattice dynamics and elasticity Alexander, Shlomo Physics Reports, Vol. 296, Issue 2-4 https://doi.org/10.1016/S0370-1573(97)00069-0	journal	March 1998
Dynamics near Free Surfaces and the Glass Transition in Thin Polymer Films: A View to the Future Ediger, M. D.; Forrest, J. A. Macromolecules, Vol. 47, Issue 2 https://doi.org/10.1021/ma4017696	journal	November 2013
Nanometallic Glasses: Size Reduction Brings Ductility, Surface State Drives Its Extent Chen, D. Z.; Jang, D.; Guan, K. M. Nano Letters, Vol. 13, Issue 9 https://doi.org/10.1021/nl402384r	journal	August 2013
Irreversible reorganization in a supercooled liquid originates from localized soft modes Widmer-Cooper, Asaph; Perry, Heidi; Harrowell, Peter Nature Physics, Vol. 4, Issue 9 https://doi.org/10.1038/nphys1025	journal	July 2008
Phonon gap and localization lengths in floppy materials Düring, Gustavo; Lerner, Edan; Wyart, Matthieu Soft Matter, Vol. 9, Issue 1 https://doi.org/10.1039/C2SM25878A	journal	January 2013
Strain localization in glassy polymers under cylindrical confinement Shavit, Amit; Riggleman, Robert A. Physical Chemistry Chemical Physics, Vol. 16, Issue 22 https://doi.org/10.1039/c3cp55330b	journal	January 2014
Stability of jammed packings I: the rigidity length scale Goodrich, Carl P.; Ellenbroek, Wouter G.; Liu, Andrea J. Soft Matter, Vol. 9, Issue 46 https://doi.org/10.1039/c3sm51095f	journal	January 2013
Stability of jammed packings II: the transverse length scale Schoenholz, Samuel S.; Goodrich, Carl P.; Kogan, Oleg Soft Matter, Vol. 9, Issue 46 https://doi.org/10.1039/c3sm51096d	journal	January 2013
Breakdown of continuum elasticity in amorphous solids Lerner, Edan; DeGiuli, Eric; Düring, Gustavo Soft Matter, Vol. 10, Issue 28 https://doi.org/10.1039/c4sm00311j	journal	January 2014
On the rigidity of amorphous solids Wyart, M. Annales de Physique, Vol. 30, Issue 3 https://doi.org/10.1051/anphys:2006003	journal	January 2005
Influence of confinement on the vibrational density of states and the Boson peak in a polymer glass Jain, Tushar S.; de Pablo, Juan J. The Journal of Chemical Physics, Vol. 120, Issue 19 https://doi.org/10.1063/1.1689952	journal	May 2004
Finite-size effects in the phonon density of states of nanostructured germanium: A comparative study of nanoparticles, nanocrystals, nanoglasses, and bulk phases Şopu, D.; Kotakoski, J.; Albe, K. Physical Review B, Vol. 83, Issue 24 https://doi.org/10.1103/PhysRevB.83.245416	journal	June 2011
Jamming at zero temperature and zero applied stress: The epitome of disorder O’Hern, Corey S.; Silbert, Leonardo E.; Liu, Andrea J. Physical Review E, Vol. 68, Issue 1 https://doi.org/10.1103/PhysRevE.68.011306	journal	July 2003
Effects of compression on the vibrational modes of marginally jammed solids Wyart, Matthieu; Silbert, Leonardo E.; Nagel, Sidney R. Physical Review E, Vol. 72, Issue 5 https://doi.org/10.1103/PhysRevE.72.051306	journal	November 2005
Heat transport in model jammed solids Vitelli, Vincenzo; Xu, Ning; Wyart, Matthieu Physical Review E, Vol. 81, Issue 2 https://doi.org/10.1103/PhysRevE.81.021301	journal	February 2010
Contact nonlinearities and linear response in jammed particulate packings Goodrich, Carl P.; Liu, Andrea J.; Nagel, Sidney R. Physical Review E, Vol. 90, Issue 2 https://doi.org/10.1103/PhysRevE.90.022201	journal	August 2014
Nonperturbative Effect of Attractive Forces in Viscous Liquids Berthier, Ludovic; Tarjus, Gilles Physical Review Letters, Vol. 103, Issue 17 https://doi.org/10.1103/PhysRevLett.103.170601	journal	October 2009
Vibrational Modes Identify Soft Spots in a Sheared Disordered Packing Manning, M. L.; Liu, A. J. Physical Review Letters, Vol. 107, Issue 10 https://doi.org/10.1103/PhysRevLett.107.108302	journal	August 2011
Information-Theoretic Measurements of Coupling between Structure and Dynamics in Glass Formers Jack, Robert L.; Dunleavy, Andrew J.; Royall, C. Patrick Physical Review Letters, Vol. 113, Issue 9 https://doi.org/10.1103/PhysRevLett.113.095703	journal	August 2014
Vibrations and Diverging Length Scales Near the Unjamming Transition Silbert, Leonardo E.; Liu, Andrea J.; Nagel, Sidney R. Physical Review Letters, Vol. 95, Issue 9 https://doi.org/10.1103/PhysRevLett.95.098301	journal	August 2005
Predicting the Long-Time Dynamic Heterogeneity in a Supercooled Liquid on the Basis of Short-Time Heterogeneities Widmer-Cooper, Asaph; Harrowell, Peter Physical Review Letters, Vol. 96, Issue 18 https://doi.org/10.1103/PhysRevLett.96.185701	journal	May 2006
Structural Relaxation Made Simple Bitzek, Erik; Koskinen, Pekka; Gähler, Franz Physical Review Letters, Vol. 97, Issue 17 https://doi.org/10.1103/PhysRevLett.97.170201	journal	October 2006
Critical Scaling in Linear Response of Frictionless Granular Packings near Jamming Ellenbroek, Wouter G.; Somfai, Ellák; van Hecke, Martin Physical Review Letters, Vol. 97, Issue 25 https://doi.org/10.1103/PhysRevLett.97.258001	journal	December 2006
Excess Vibrational Modes and the Boson Peak in Model Glasses Xu, Ning; Wyart, Matthieu; Liu, Andrea J. Physical Review Letters, Vol. 98, Issue 17 https://doi.org/10.1103/PhysRevLett.98.175502	journal	April 2007
Anharmonic and quasi-localized vibrations in jammed solids—Modes for mechanical failure Xu, N.; Vitelli, V.; Liu, A. J. EPL (Europhysics Letters), Vol. 90, Issue 5 https://doi.org/10.1209/0295-5075/90/56001	journal	June 2010
Geometric origin of excess low-frequency vibrational modes in weakly connected amorphous solids Wyart, M.; Nagel, S. R.; Witten, T. A. Europhysics Letters (EPL), Vol. 72, Issue 3 https://doi.org/10.1209/epl/i2005-10245-5	journal	November 2005

Cited By (5)

Spatial structure of states of self stress in jammed systems Sussman, Daniel M.; Goodrich, Carl P.; Liu, Andrea J. Soft Matter, Vol. 12, Issue 17 https://doi.org/10.1039/c6sm00094k	journal	January 2016
Topological boundary modes in jammed matter Sussman, Daniel M.; Stenull, Olaf; Lubensky, T. C. Soft Matter, Vol. 12, Issue 28 https://doi.org/10.1039/c6sm00875e	journal	January 2016
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Disentangling defects and sound modes in disordered solids Wijtmans, Sven; Manning, M. Lisa arXiv https://doi.org/10.48550/arxiv.1502.00685	preprint	January 2015
Topological boundary modes in jammed matter Sussman, Daniel M.; Stenull, Olaf; Lubensky, T. C. arXiv https://doi.org/10.48550/arxiv.1512.04480	text	January 2015

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36 MATERIALS SCIENCE
Surface vibrations
jammed packings
disorder

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References (27)

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