Percolation of disordered jammed sphere packings

Source abstract

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 versus 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, 0.311 608, 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.