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arXiv · 1611.00279

Percolation of disordered jammed sphere packings

Robert M. Ziff·Salvatore Torquato
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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 $φ$, the threshold corresponds to a critical value $φ_c = 0.199$. 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.

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Robert M. Ziff, Salvatore Torquato. 2016-11-01. Percolation of disordered jammed sphere packings. https://doi.org/10.1088/1751-8121%2Faa5664

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