Department of Chemistry, Philipps-Universität Marburg, Hans-Meerwein-Strasse 4, D-35032 Marburg, Germany.
Soft Matter. 2016 May 7;12(17):3991-4006. doi: 10.1039/c6sm00567e. Epub 2016 Mar 29.
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.
我们将 Widom 粒子插入法[B. Widom, J. Chem. Phys., 1963, 39, 2808-2812]扩展到确定摩擦硬球堆积中爱德华兹熵的上限 sub。sub 对应于给定体积分数和边界条件下力学稳定构型数量的对数。为了实现这一目标，我们将用于估计无摩擦堆积中通过孔径分布的粒子插入概率的方法[V. Baranau, et al., Soft Matter, 2013, 9, 3361-3372]扩展到摩擦粒子的情况。我们使用计算机生成和实验获得的三维球体堆积，体积分数φ在 0.551-0.65 范围内。我们发现 sub 在随机疏松堆积极限φ RLP = 0.55 附近具有最大值，然后随着 φ 的增加单调减小，在φ = 0.65 时达到最小值。此外，sub 不能区分实际力学稳定性和接近力学稳定构型的堆积。在足够大的孔中插入一个粒子时找到给定数量的接触的概率与 φ 无关，但随着接触数量的增加而强烈减小。
