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Jamming at zero temperature and zero applied stress: The epitome of disorder

2003/04/17 by C. S. O'Hern, Corey S. O’Hern, Leonardo E. Silbert +5 · 150 citations
Engineering · Materials Science · Physics and Astronomy · #Granular flow and fluidized beds #Material Dynamics and Properties #Theoretical and Computational Physics #cond-mat.soft

paper · pdf · doi:10.1103/physreve.68.011306

published as Phys. Rev. E 68, 011306 (2003) · 21 pages, 20 figures

arxiv created 2003/04/17 · openalex publication_date 2003/07/25 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31

Abstract

We have studied how two- and three-dimensional systems made up of particles interacting with finite range, repulsive potentials jam (i.e., develop a yield stress in a disordered state) at zero temperature and zero applied stress. At low packing fractions phi, the system is not jammed and each particle can move without impediment from its neighbors. For each configuration, there is a unique jamming threshold phi(c) at which particles can no longer avoid each other, and the bulk and shear moduli simultaneously become nonzero. The distribution of phi(c) values becomes narrower as the system size increases, so that essentially all configurations jam at the same packing fraction in the thermodynamic limit. This packing fraction corresponds to the previously measured value for random close packing. In fact, our results provide a well-defined meaning for "random close packing" in terms of the fraction of all phase space with inherent structures that jam. The jamming threshold, point J, occurring at zero temperature and applied stress and at the random-close-packing density, has properties reminiscent of an ordinary critical point. As point J is approached from higher packing fractions, power-law scaling is found for the divergence of the first peak in the pair correlation function and in the vanishing of the pressure, shear modulus, and excess number of overlapping neighbors. Moreover, near point J, certain quantities no longer self-average, suggesting the existence of a length scale that diverges at J. However, point J also differs from an ordinary critical point: the scaling exponents do not depend on dimension but do depend on the interparticle potential. Finally, as point J is approached from high packing fractions, the density of vibrational states develops a large excess of low-frequency modes. Indeed, at point J, the density of states is a constant all the way down to zero frequency. All of these results suggest that point J is a point of maximal disorder and may control behavior in its vicinity-perhaps even at the glass transition.

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