Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 3500 MB Eindhoven, The Netherlands.
Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, 79104 Freiburg, Germany.
Phys Rev E. 2019 Dec;100(6-1):062129. doi: 10.1103/PhysRevE.100.062129.
We investigate by means of continuum percolation theory and Monte Carlo simulations how spontaneous uniaxial symmetry breaking affects geometric percolation in dispersions of hard rodlike particles. If the particle aspect ratio exceeds about 20, percolation in the nematic phase can be lost upon adding particles to the dispersion. This contrasts with percolation in the isotropic phase, where a minimum particle loading is always required to obtain system-spanning clusters. For sufficiently short rods, percolation in the uniaxial nematic mimics that of the isotropic phase, where the addition of particles always aids percolation. For aspect ratios between 20 and infinity, but not including infinity, we find reentrance behavior: percolation in the low-density nematic may be lost upon increasing the amount of nanofillers but can be regained by the addition of even more particles to the suspension. Our simulation results for aspect ratios of 5, 10, 20, 50, and 100 strongly support our theoretical predictions, with almost quantitative agreement. We show that a different closure of the connectedness Ornstein-Zernike equation, inspired by scaled particle theory, is as least as accurate in predicting the percolation threshold as the Parsons-Lee closure, which effectively describes the impact of many-body direct contacts.
我们通过连续体渗流理论和蒙特卡罗模拟研究了自发单轴对称破缺如何影响硬棒状粒子分散体中的几何渗流。如果粒子的纵横比超过 20，在向分散体中添加粒子时，向列相中的渗流可能会丢失。这与各向同性相中相反，在各向同性相中，总是需要最低限度的粒子负载才能获得系统跨越的团簇。对于足够短的棒，单轴向列相中的渗流类似于各向同性相中的渗流，其中总是添加粒子有助于渗流。对于纵横比在 20 到无穷大之间，但不包括无穷大的情况，我们发现了再入行为：在低密度向列相中，渗流可能会在增加纳米填料的量时丢失，但通过向悬浮液中添加更多的粒子可以重新获得。我们对纵横比为 5、10、20、50 和 100 的模拟结果强烈支持我们的理论预测，几乎完全一致。我们表明，受粒子理论启发的不同连接性奥恩斯坦-泽尔尼克方程的封闭形式在预测渗流阈值方面与帕森斯-李封闭形式一样准确，后者有效地描述了多体直接接触的影响。
