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.

中文翻译：

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硬血小板悬浮液中团簇的形状，几何渗透和电导率

使用蒙特卡洛模拟，我们研究了硬质血小板悬浮液中的几何渗透和电导率如何受到血小板添加及其自发排列程度的影响。在纵横比为10、25和50的模拟结果中，我们始终观察到作为体积分数的函数的单调下降的渗滤阈值，即添加颗粒始终有助于渗滤。在向列相中，渗流团簇内部的颗粒分布变得不那么球形对称，并且团簇的纵横比增加。然而，尽管簇的纵横比根据体积分数保持恒定，并且仅微弱地依赖于颗粒的纵横比，但簇在各向同性相中也呈各向异性形状。将血小板的渗流簇映射到线性电阻器网络，并将单元电导分配给所有连接，我们发现在各向同性-向列相变以及各个稳定相中均具有恒定的电导率。此行为与网络中其他观察到的拓扑特性一致，即平均路径长度，每个粒子的平均接触数和基尔霍夫指数，它们均保持不变，并且不受粒子添加和排列程度的影响他们的停权。相反，使用各向异性电导模型明确说明粒子的相对取向，则网络电导率随各向同性中体积分数的增加而降低，并在向列相的开始时进一步减少，同时在向列相的深处保持相同的趋势。因此，我们的观察一致地表明，与棒状填充剂不同，由血小板悬浮液产生的网络结构对颗粒的长径比或取向不是很敏感。因此，血小板不像填充剂那样通用，可以分散在导电复合材料中。