title: Upper bound on the Edwards entropy in frictional monodisperse hard-sphere packings.
abstract: We extend the Widom particle insertion method [B. Widom, J. Chem. Phys., 1963, 39, 2808-2812] to determine an upper bound sub on the Edwards entropy in frictional hard-sphere packings. sub 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 sub has a maximum in the vicinity of the Random Loose Packing Limit φRLP = 0.55 and decreases then monotonically with increasing φ to reach a minimum at φ = 0.65. Further on, sub 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.
authors.affiliation: Department of Chemistry, Philipps-Universität Marburg, Hans-Meerwein-Strasse 4, D-35032 Marburg, Germany. tallarek@staff.uni-marburg.de.
authors.forename: Vasili
authors.initials: V
authors.lastname: Baranau
authors.forename: Song-Chuan
authors.initials: SC
authors.lastname: Zhao
authors.forename: Mario
authors.initials: M
authors.lastname: Scheel
authors.forename: Ulrich
authors.initials: U
authors.lastname: Tallarek
authors.forename: Matthias
authors.initials: M
authors.lastname: Schröter