Packing of Spheres: Co-ordination of Randomly Packed Spheres

Bernal, J. D.; Mason, Jan

doi:10.1038/188910a0

Cited by 938 publications

(488 citation statements)

References 2 publications

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“…4 shows that the average number of contacts on a sphere, the coordination number, hCi is indeed greater than 4 for all x 2 . The monodisperse case has hCi ¼ 5:812, in agreement with previous studies [4,7]. In this monodisperse case it is believed that the average number of contacts is close to six contacting spheres [4]; each sphere is resting on three spheres and are supporting three other.…”

Section: Contact Numberssupporting

confidence: 77%

“…On larger length scales, however, as in experiments on ball bearings, preferable sedimentation direction is present. In this length scale there exist different methods to find hCi and to determine the caging effect [4,20]. The difference in packing procedure may cause different restructuring rules during the contraction and changes thus the caging procedure.…”

Section: Cagingmentioning

confidence: 99%

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Simulation of random packing of binary sphere mixtures by mechanical contraction

Kristiansen

Wouterse

Philipse

2005

Physica A: Statistical Mechanics and its Applications

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The mechanical contraction simulation for random dense packings is extended to binary mixture of spheres. The volume packing density as a function of sphere composition follows a characteristic triangular shape and resembles previous experiments on length scales from colloidal particles to metal shots. An excluded volume argument, which qualitatively explains trends in random packing densities of monodisperse particles, is insufficient to account for this triangular shape. The coordination number, or the average number of contacts on a sphere, shows a remarkable dip from 6 to 4 at the crossover from many small spheres to many large spheres, which has not been reported earlier. An explanation is given in terms of caging effects. r

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Section: Contact Numberssupporting

confidence: 77%

Section: Cagingmentioning

confidence: 99%

Simulation of random packing of binary sphere mixtures by mechanical contraction

Kristiansen

Wouterse

Philipse

2005

Physica A: Statistical Mechanics and its Applications

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“…with the random closed packed density, ρ * RCP , = 1.21658 57,58 . While the Carnahan-Starling equation of state gives accurate values for the free energy at moderately high densities, this is not true for the other two equations of state used in this work.…”

Section: Liquid State Thermodynamics and The Potentialmentioning

confidence: 99%

Intermolecular Forces and the Glass Transition

Hall

Wolynes

2007

J. Phys. Chem. B

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Random first order transition theory is used to determine the role of attractive and repulsive interactions in the dynamics of supercooled liquids. Self-consistent phonon theory, an approximate mean field treatment consistent with random first order transition theory, is used to treat individual glassy configurations, while the liquid phase is treated using common liquid state approximations.Free energies are calculated using liquid state perturbation theory. The transition temperature T * A , the temperature where the onset of activated behavior is predicted by mean field theory, the lower crossover temperature T * c where barrierless motions actually occur through fractal or stringy motions (corresponding to the phenomenological mode coupling transition temperature), and T * K , the Kauzmann temperature (corresponding to an extrapolated entropy crisis), are calculated in addition to T * g , the glass transition temperature that corresponds to laboratory cooling rates. Relationships between these quantities agree well with existing experimental and simulation data on van der Waals liquids. Both the isobaric and isochoric behavior in the supercooled regime are studied, providing results for ∆C V and ∆C p that can be used to calculate the fragility as a function of density and pressure, respectively. The predicted variations in the α-relaxation time with temperature and density conform to the empirical density-temperature scaling relations found by Casalini and Roland. We thereby demonstrate the microscopic origin of their observations. Finally, the relationship first suggested by Sastry between the spinodal temperature and the Kauzmann temperatures, as a function of density, is examined. The present microscopic calculations support the existence of an intersection of these two temperatures at sufficiently low temperatures.2

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“…3: A fractional power law divergence at or near the "random close packed" density η rcp = 0.64 as defined by [61,62,63,64] These approximates are obtained from a D-log Padé analysis and are (generalizations) of the form…”

Section: Approximate Equations Of State For Hard Spheresmentioning

confidence: 99%

Negative Virial Coefficients and the Dominance of Loose Packed Diagrams for D-Dimensional Hard Spheres

Clisby

McCoy

2004

Journal of Statistical Physics

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We study the virial coefficients B k of hard spheres in D dimensions by means of Monte-Carlo integration. We find that B5 is positive in all dimensions but that B6 is negative for all D ≥ 6. For 7 ≤ k ≤ 17 we compute sets of Ree-Hoover diagrams and find that either for large D or large k the dominant diagrams are "loose packed". We use these results to study the radius of convergence and the validity of the many approximations used for the equations of state for hard spheres.

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Packing of Spheres: Co-ordination of Randomly Packed Spheres

Cited by 938 publications

References 2 publications

Simulation of random packing of binary sphere mixtures by mechanical contraction

Simulation of random packing of binary sphere mixtures by mechanical contraction

Intermolecular Forces and the Glass Transition

Negative Virial Coefficients and the Dominance of Loose Packed Diagrams for D-Dimensional Hard Spheres

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