Percolation of disordered jammed sphere packings

Abstract

We determine the site and bond percolation thresholds for a system of disordered jammed sphere packings in the maximally random jammed state, generated by the Torquato-Jiao algorithm. For the site threshold, which gives the fraction of conducting vs. non-conducting spheres necessary for percolation, we find $p_c=0.3116(3)$, consistent with the 1979 value of Powell $0.310(5)$ and identical within errors to the threshold for the simple-cubic lattice, 0.311608, which shares the same average coordination number of 6. In terms of the volume fraction $\phi$, the threshold corresponds to a critical value ${\phi }_c=0.199$. For the bond threshold, which apparently was not measured before, we find $p_c=0.2424(3)$. To find these thresholds, we considered two shape-dependent universal ratios involving the size of the largest cluster, fluctuations in that size, and the second moment of the size distribution; we confirmed the ratios' universality by also studying the simple-cubic lattice with a similar cubic boundary. The results are applicable to many problems including conductivity in random mixtures, glass formation, and drug loading in pharmaceutical tablets.

8 pages including references

References in corpus (8)

• Robust Algorithm to Generate a Diverse Class of Dense Disordered and Ordered Sphere Packings via Linear Programming
• Equilibrium Phase Behavior and Maximally Random Jammed State of Truncated Tetrahedra
• Non-Universality of Density and Disorder in Jammed Sphere Packings
• Simple cubic random-site percolation thresholds for neighborhoods containing fourth-nearest neighbors
• Finite-size scaling of the stochastic susceptible-infected-recovered model
• Dimer percolation and jamming on simple cubic lattice
• Short-range correlations in percolation at criticality
• Jamming and percolation of parallel squares in single-cluster growth model

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