Logan Jack A, Tkachenko Alexei V
Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794, USA.
Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, USA.
Phys Rev E. 2022 Jan;105(1-1):014117. doi: 10.1103/PhysRevE.105.014117.
We present a statistical mechanical description of randomly packed spherical particles, where the average coordination number is treated as a macroscopic thermodynamic variable. The overall packing entropy is shown to have two contributions: geometric, reflecting statistical weights of individual configurations, and topological, which corresponds to the number of topologically distinct states. Both of them are computed in the thermodynamic limit for isostatic and weakly underconstrained packings in 2D and 3D. The theory generalizes concepts of granular and glassy configurational entropies for the case of nonjammed systems. It is directly applicable to sticky colloids and predicts an asymptotic phase behavior of sticky spheres in the limit of strong binding.
我们给出了随机堆积球形颗粒的统计力学描述，其中平均配位数被视为一个宏观热力学变量。整体堆积熵显示有两种贡献：几何贡献，反映单个构型的统计权重；拓扑贡献，对应拓扑不同状态的数量。它们都在二维和三维等静压和弱欠约束堆积的热力学极限下进行计算。该理论将颗粒和玻璃态构型熵的概念推广到非堵塞系统的情况。它直接适用于粘性胶体，并预测了强结合极限下粘性球体的渐近相行为。
