On the rigidity of a hard-sphere glass near random close packingC. Brito1, 2 and M. Wyart3, 2
1 Instituto de Física, Universidade Federal do Rio Grande do Sul 91501-970 Porto Alegre, Brazil
2 CEA - Service de Physique de l'Etat Condensé, Centre d'Etudes de Saclay 91191 Gif-sur-Yvette, France
3 Division of Engineering and Applied Sciences, Harvard University, Pierce Hall 29 Oxford Street, Cambridge, MA 02138, USA
received 24 March 2006; accepted in final form 10 August 2006
published online 30 August 2006
We study theoretically and numerically the microscopic cause of the rigidity of hard-sphere glasses near their maximum packing. We show that, after coarse-graining over time, the hard-sphere interaction can be described by an effective potential which is exactly logarithmic at the random close packing . This allows to define normal modes, and to apply recent results valid for elastic networks: rigidity is a non-local property of the packing geometry, and is characterized by some length scale l* which diverges at (WYART M., NAGEL S. R. and WITTEN T. A., Europhys. Lett., 72 (2005) 486; WYART M., SILBERT L. E., NAGEL S. R. and WITTEN T. A., Phys. Rev. E, 72 (2005) 051306). We compute the scaling of the bulk and shear moduli near , and speculate on the possible implications of these results for the glass transition.
81.05.Rm - Porous materials; granular materials.
82.70.-y - Disperse systems; complex fluids.
64.70.Pf - Glass transitions.
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