Atashpendar Arshia, Ingenbrand Tim, Schilling Tanja
Institute of Physics, University of Freiburg, Hermann-Herder-Straße 3, 79104 Freiburg, Germany.
Phys Rev E. 2020 Mar;101(3-1):032706. doi: 10.1103/PhysRevE.101.032706.
Using Monte Carlo simulations, we investigate how geometric percolation and electrical conductivity in suspensions of hard conducting platelets are affected by the addition of platelets and their degree of spontaneous alignment. In our simulation results for aspect ratios 10, 25, and 50, we consistently observe a monotonically decreasing percolation threshold as a function of volume fraction, i.e., the addition of particles always aids percolation. In the nematic phase, the distribution of particles inside the percolating clusters becomes less spherically symmetric and the aspect ratio of the clusters increases. However, the clusters are also anisotropically shaped in the isotropic phase, although their aspect ratio remains constant as a function of volume fraction and is only weakly dependent on the particle aspect ratio. Mapping the percolating clusters of platelets to linear resistor networks, and assigning unit conductance to all connections, we find a constant conductivity both across the isotropic-nematic transition and in the respective stable phases. This behavior is consistent with the other observed topological properties of the networks, namely, the average path length, average number of contacts per particle, and the Kirchhoff index, which all remain constant and unaffected by both the addition of particles and the degree of alignment of their suspension. In contrast, using an anisotropic conductance model that explicitly accounts for the relative orientation of the particles, the network conductivity decreases with increasing volume fraction in the isotropic, and further diminishes at the onset of the nematic while preserving the same trend deep in the nematic. Hence, our observations consistently suggest that, unlike for rodlike fillers, the network structures that arise from platelet suspensions are not very sensitive to the particle aspect ratio or to alignment. Hence platelets are not as versatile as fillers for dispersion in conductive composite materials as rods.
通过蒙特卡罗模拟，我们研究了添加硬导电片状颗粒及其自发排列程度如何影响硬导电片状颗粒悬浮液中的几何渗流和电导率。在我们针对长径比为10、25和50的模拟结果中，我们始终观察到渗流阈值随体积分数单调下降，即添加颗粒总是有助于渗流。在向列相中，渗流团簇内颗粒的分布变得不那么球对称，团簇的长径比增加。然而，在各向同性相中团簇也呈各向异性形状，尽管它们的长径比随体积分数保持不变，且仅微弱地依赖于颗粒长径比。将片状颗粒的渗流团簇映射到线性电阻网络，并为所有连接赋予单位电导，我们发现在各向同性 - 向列相转变以及各自的稳定相中电导率都是恒定的。这种行为与网络的其他观察到的拓扑性质一致，即平均路径长度、每个颗粒的平均接触数和基尔霍夫指数，这些都保持不变，并且不受颗粒添加及其悬浮液排列程度的影响。相比之下，使用明确考虑颗粒相对取向的各向异性电导模型，网络电导率在各向同性相中随体积分数增加而降低，并在向列相开始时进一步减小，同时在向列相深处保持相同趋势。因此，我们的观察结果一致表明，与棒状填料不同，片状颗粒悬浮液产生的网络结构对颗粒长径比或排列不太敏感。因此，片状颗粒作为导电复合材料中的分散填料不如棒状颗粒通用。
