A simple effective rule to estimate the jamming packing fraction of polydisperse hard spheres

Abstract

A recent proposal in which the equation of state of a polydisperse hard-sphere mixture is mapped onto that of the one-component fluid is extrapolated beyond the freezing point to estimate the jamming packing fraction ${\varphi }_{\text{J}}$ of the polydisperse system as a simple function of $M_1{M}_3/M_2^2$, where $M_k$ is the $k$th moment of the size distribution. An analysis of experimental and simulation data of ${\varphi }_{\text{J}}$ for a large number of different mixtures shows a remarkable general agreement with the theoretical estimate. To give extra support to the procedure, simulation data for seventeen mixtures in the high-density region are used to infer the equation of state of the pure hard-sphere system in the metastable region. An excellent collapse of the inferred curves up to the glass transition and a significant narrowing of the different out-of-equilibrium glass branches all the way to jamming are observed. Thus, the present approach provides an extremely simple criterion to unify in a common framework and to give coherence to data coming from very different polydisperse hard-sphere mixtures.

5 pages, 3 figures; v2: slight changes plus new references

References in corpus (9)

• Influence of Particle Size Distribution on Random Close Packing
• Crystallization of hard-sphere glasses
• Why is Random Close Packing Reproducible?
• Pushing the glass transition towards random close packing using self-propelled hard spheres
• Avalanches mediate crystallization in a hard-sphere glass
• Equilibrium equation of state of a hard sphere binary mixture at very large densities using replica exchange Monte-Carlo simulations
• Class of consistent fundamental-measure free energies for hard-sphere mixtures
• Note: An exact scaling relation for truncatable free energies of polydisperse hard-sphere mixtures
• A note on rattlers in amorphous packings of binary mixtures of hard spheres

Cited by in corpus (12)

• Influence of Particle Size Distribution on Random Close Packing
• Structural and Thermodynamic Properties of Hard-Sphere Fluids
• Sub-Jamming Transition in Binary Sphere Mixtures
• Equation of state of polydisperse hard-disk mixtures in the high-density regime
• Chemical potential of a test hard sphere of variable size in hard-sphere fluid mixtures
• Equation of State of Four- and Five-Dimensional Hard-Hypersphere Mixtures
• Discontinuous Shear Thickening (DST) transition with spherical iron particles coated by adsorbed brush polymer
• Influence of the Long-Range Forces in Non-Gaussian Random-Packing Dynamics
• A heuristic approach for the densest packing fraction of hard-sphere mixtures
• Protein folding as a jamming transition
• Effects of the long-range cohesive forces in binary particle packing dynamics
• Predicting random close packing of binary hard-disk mixtures via third-virial-based parameters