# A phase diagram for jammed matter

@article{Song2008APD, title={A phase diagram for jammed matter}, author={Chaoming Song and Peng-xin Wang and Hern{\'a}n A. Makse}, journal={Nature}, year={2008}, volume={453}, pages={629-632} }

The problem of finding the most efficient way to pack spheres has a long history, dating back to the crystalline arrays conjectured by Kepler and the random geometries explored by Bernal. Apart from its mathematical interest, the problem has practical relevance in a wide range of fields, from granular processing to fruit packing. There are currently numerous experiments showing that the loosest way to pack spheres (random loose packing) gives a density of ∼55 per cent. On the other hand, the…

## Figures, Tables, and Topics from this paper

## 695 Citations

A first-order phase transition defines the random close packing of hard spheres

- Physics, Materials Science
- 2010

Randomly packing spheres of equal size into a container consistently results in a static configuration with a density of ∼64%. The ubiquity of random close packing (RCP) rather than the optimal…

Jammed hard-particle packings: From Kepler to Bernal and beyond

- Physics
- 2010

This review describes the diversity of jammed configurations attainable by frictionless convex nonoverlapping (hard) particles in Euclidean spaces and for that purpose it stresses individual-packing…

Mean-field theory of random close packings of axisymmetric particles.

- Mathematics, PhysicsNature communications
- 2013

A mean-field formalism is presented to estimate the packing density of axisymmetric non-spherical particles, derived from an analytic continuation from the sphere that provides a phase diagram predicting that, for the same coordination number, the density of monodisperse random packings follows the sequence of increasing packing fractions.

Statistical theory of correlations in random packings of hard particles.

- Medicine, MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2014

This work takes inspiration from liquid theories for the n-particle angular correlation function to develop a formalism of random packings of hard particles from the bottom up and predicts the density of two-dimensional random close packing and random loose packing.

A Geometric-Structure Theory for Maximally Random Jammed Packings

- Physics, Computer ScienceScientific reports
- 2015

This work derives for the first time a highly accurate formula for MRJ densities for a very wide class of two-dimensional frictionless packings, namely, binary convex superdisks, with shapes that continuously interpolate between circles and squares, by incorporating specific attributes of MRJ states and a novel organizing principle.

Close packing density of polydisperse hard spheres.

- Physics, MedicineThe Journal of chemical physics
- 2009

The theory agrees well with the simulations for bidisperse, tridisperse, and log-normal distributions and correctly reproduces the exact limits for large size ratios.

Model for random packing of polydisperse frictionless spheres

- Physics
- 2010

We propose a statistical model for the random packing of frictionless polydisperse spheres in which the complexity of the global packing is distilled into a local stochastic process. We simplify the…

Attractive emulsion droplets probe the phase diagram of jammed granular matter

- Chemistry, MedicineProceedings of the National Academy of Sciences
- 2011

Within the Edwards statistical mechanics framework, this result measures the decrease in compactivity with global density, which represents a direct experimental test of a jamming phase diagram in athermal systems and gives support to the much-debated statistical physics of jammed granular matter.

Cavity method for force transmission in jammed disordered packings of hard particles.

- Physics, MedicineSoft matter
- 2014

A mean-field theory is developed for jammed disordered packings based on the consideration of the contact network as a random graph where the force transmission becomes a constraint satisfaction problem, and a new signature of jamming is found in the small force behavior.

Dense packing in the monodisperse hard-sphere system: A numerical study

- Materials Science, MedicineThe European physical journal. E, Soft matter
- 2010

This work provides quantitative evidence for the claim that the density and structural order of the arrested close packing can be determined by the compression rate, i.e., with slower rates producing denser and more ordered structures.

## References

SHOWING 1-10 OF 42 REFERENCES

The density of random close packing of spheres

- Physics
- 1969

Models of randomly packed hard spheres exhibit some features of the properties of simple liquids, e.g. the packing density and the radial distribution. The value of the maximum packing density of…

Multiplicity of Generation, Selection, and Classification Procedures for Jammed Hard-Particle Packings †

- Computer Science, Physics
- 2001

It is shown that there is a multiplicity of generation, selection, and classification procedures for jammed configurations of identical d-dimensional spheres, and the concept of rigidity percolation can be generalized to network glasses.

Jamming V: Jamming in two-dimensional packings

- Physics
- 2008

We investigate the existence of random close and random loose packing limits in two-dimensional packings of monodisperse hard disks. A statistical mechanics approach-- based on several approximations…

Is random close packing of spheres well defined?

- Physics, MedicinePhysical review letters
- 2000

It is argued that the current picture of RCP cannot be made mathematically precise and support this conclusion via a molecular dynamics study of hard spheres using the Lubachevsky-Stillinger compression algorithm.

A Landscape Analysis of Constraint Satisfaction Problems

- Mathematics, Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

An analysis of constraint satisfaction problems, such as sphere packing, K-SAT, and graph coloring, in terms of an effective energy landscape is discussed, to better characterize the J-point, proposed as a systematic definition of random close packing, and to place it in the context of other theories of glasses.

The ideal glass transition of hard spheres.

- Materials Science, MedicineThe Journal of chemical physics
- 2005

The replica method is used to study the ideal glass transition of a liquid of identical hard spheres and it is found that the mean coordination number at phi(c) is equal to 6.

Local and global relations between the number of contacts and density in monodisperse sphere packs

- Materials Science, Physics
- 2006

The topological structure resulting from the network of contacts between grains (contact network) is studied for large samples of monosized spheres with densities (fraction of volume occupied by the…

Statistical mechanics of jammed matter

- Physics
- 2004

Jamming refers to a state which emerges when a many-body system is blocked in a static configuration far from equilibrium. It has been postulated that the behavior of systems experiencing such a…

Packing of compressible granular materials

- Medicine, PhysicsPhysical review letters
- 2000

3D computer simulations and experiments are employed to study random packings of compressible spherical grains under external confining stress. In the rigid ball limit, we find a continuous…

Density fluctuations in vibrated granular materials

- Materials Science
- 1998

We report systematic measurements of the density of a vibrated granular material as a function of time. Monodisperse spherical beads were confined to a cylindrical container and shaken vertically.…