Upper bound on the Edwards entropy in frictional monodisperse hard-sphere packings - Schröter, Matthias; Baranau, Vasili; Zhao, Song-Chuan; Scheel, Mario; Tallarek, Ulrich (Soft Matter, 2016)
We extend the Widom particle insertion method [B. Widom, J. Chem. Phys., 1963, 39, 2808-2812] to determine an upper bound s on the Edwards entropy in frictional hard-sphere packings. s corresponds to the logarithm of the number of mechanically stable configurations for a given volume fraction and boundary conditions. To accomplish this, we extend the method for estimating the particle insertion probability through the pore-size distribution in frictionless packings [V. Baranau, et al., Soft Matter, 2013, 9, 3361-3372] to the case of frictional particles. We use computer-generated and experimentally obtained three-dimensional sphere packings with volume fractions φ in the range 0.551-0.65. We find that s has a maximum in the vicinity of the Random Loose Packing Limit φ = 0.55 and decreases then monotonically with increasing φ to reach a minimum at φ = 0.65. Further on, s does not distinguish between real mechanical stability and packings in close proximity to mechanical stable configurations. The probability to find a given number of contacts for a particle inserted in a large enough pore does not depend on φ, but it decreases strongly with the contact number.