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

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

2005-12-09

arxiv.org/abs/cond-mat/0512197v4

Europhys. Lett., 76 (1), pp. 149-155 (2006)

Physics

Condensed Matter

Soft Condensed Matter

7 pages, 4 figures. Figure 4 had a wrong unit in abscissa, which was corrected

Scientific paper

10.1209/epl/i2006-10238-x

We study theoretically and numerically the microscopic cause of the mechanical stability 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 $\phi_c$. This allows to define normal modes, and to apply recent results valid for elastic networks: mechanical stability is a non-local property of the packing geometry, and is characterized by some length scale $l^*$ which diverges at $\phi_c$ [1, 2]. We compute the scaling of the bulk and shear moduli near $\phi_c$, and speculate on the possible implications of these results for the glass transition.

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