Estimating random close packing in polydisperse and bidisperse hard spheres via an equilibrium model of crowding
Estimating random close packing in polydisperse and bidisperse hard spheres via an equilibrium model of crowding
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DOI：
10.1063/5.0137111
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发表时间：
2023-01-28
影响因子：
4.4
通讯作者：
Zaccone, Alessio
中科院分区：
文献类型：
--
作者：
Anzivino, Carmine;Casiulis, Mathias;Zaccone, Alessio
我们发现，拥挤的流体和硬球卡住的阶段之间的类比捕获的密度依赖性的接吻数为一个家庭的数值生成的卡住的状态。我们将这种类比扩展到d = 3维的硬球混合物的堵塞，因此，获得随机紧密堆积体积分数的估计，φ（RCP），作为大小多分散性的函数。我们首先考虑具有离散分布的颗粒尺寸的混合物。对于二元系统，我们使用我们自己的结果和以前的研究报告的结果，以及最近的实验从文献中的协议，我们的预测和模拟之间的协议。然后，我们将我们的方法应用于连续的多分散性系统，使用三种不同的粒度分布，即对数正态分布，伽玛分布和截断幂律分布。在所有情况下，我们观察到我们的理论研究结果和数值计算结果之间的协议相当大的多分散性的所有粒度分布时，作为参考，我们自己的模拟和结果从文献中。特别是，我们发现phi（RCP）随着分布的相对标准差s（sigma）单调增加，并在始终低于1的值处饱和。微扰展开产生了phi（RCP）的封闭形式表达式，其定量地捕获了s（sigma）< 0.5的分布无关状态。在该制度之外，我们表明，协议的逐渐损失与大小分布的偏度的增长有关。
We show that an analogy between crowding in fluid and jammed phases of hard spheres captures the density dependence of the kissing number for a family of numerically generated jammed states. We extend this analogy to jams of mixtures of hard spheres in d = 3 dimensions and, thus, obtain an estimate of the random close packing volume fraction, phi(RCP), as a function of size polydispersity. We first consider mixtures of particle sizes with discrete distributions. For binary systems, we show agreement between our predictions and simulations using both our own results and results reported in previous studies, as well as agreement with recent experiments from the literature. We then apply our approach to systems with continuous polydispersity using three different particle size distributions, namely, the log-normal, Gamma, and truncated power-law distributions. In all cases, we observe agreement between our theoretical findings and numerical results up to rather large polydispersities for all particle size distributions when using as reference our own simulations and results from the literature. In particular, we find phi(RCP) to increase monotonically with the relative standard deviation, s(sigma), of the distribution and to saturate at a value that always remains below 1. A perturbative expansion yields a closed-form expression for phi(RCP) that quantitatively captures a distribution-independent regime for s(sigma) < 0.5. Beyond that regime, we show that the gradual loss in agreement is tied to the growth of the skewness of size distributions.