Shape, geometric percolation, and electrical conductivity of clusters in suspensions of hard platelets

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.