Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel.
Department of Physics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel.
Phys Rev E. 2019 Jan;99(1-1):012146. doi: 10.1103/PhysRevE.99.012146.
The Percus-Yevick theory for monodisperse hard spheres gives very good results for the pressure and structure factor of the system in a whole range of densities that lie within the liquid phase. However, the equation seems to lead to a very unacceptable result beyond that region. Namely, the Percus-Yevick theory predicts a smooth behavior of the pressure that diverges only when the volume fraction η approaches unity. Thus, within the theory there seems to be no indication for the termination of the liquid phase and the transition to a solid or to a glass. In the present article we study the Percus-Yevick hard-sphere pair distribution function, g_{2}(r), for various spatial dimensions. We find that beyond a certain critical volume fraction η_{c}, the pair distribution function, g_{2}(r), which should be positive definite, becomes negative at some distances. We also present an intriguing observation that the critical η_{c} values we find are consistent with volume fractions where onsets of random close packing (or maximally random jammed states) are reported in the literature for various dimensions. That observation is supported by an intuitive argument. This work may have important implications for other systems for which a Percus-Yevick theory exists.
单分散硬球的 Percus-Yevick 理论在整个液相密度范围内对体系的压力和结构因子给出了非常好的结果。然而，该方程在该区域之外似乎导致了一个非常不可接受的结果。即，Percus-Yevick 理论预测压力的平滑行为，只有当体分数 η接近 1 时才会发散。因此，在该理论中，似乎没有迹象表明液相的终止以及向固体或玻璃的转变。在本文中，我们研究了各种空间维度的 Percus-Yevick 硬球对分布函数 g_2(r)。我们发现，在某个临界体分数 η_c 之后，对分布函数 g_2(r)，它应该是正定的，在某些距离处变为负。我们还提出了一个有趣的观察结果，即我们发现的临界 η_c 值与文献中报道的各种维度的随机密堆积（或最大随机堵塞状态）起始的体分数一致。这一观察结果得到了一个直观论点的支持。这项工作可能对其他存在 Percus-Yevick 理论的系统具有重要意义。
