On the rigidity of a hard-sphere glass near random close packing

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: 10 August 2006

Abstract

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.