Percolation conductivity in composites with a binary blend matrix and a non-uniform distribution of conductive sites: a lattice-based approach

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Abstract
Despite the widespread use of conductive composites with a binary blend matrix in electrical applications, computational studies examining the effects of conductive particle localization within individual phases and at their interface on conductance and the percolation threshold remain limited. To address this gap, we employ a simple cubic lattice model to simulate the localization of conductive sites within individual phases and at the interface between them. Our results show that exclusive localization of conductive sites within a single phase lowers the percolation threshold and enhances conductance, especially near the percolation threshold, whereas localization at the interface further reduces the threshold. When all conductive sites are exclusively localized in one phase, the percolation threshold can be expressed in two ways: first, as the fraction of conductive sites calculated relative to the total number of sites, denoted as Π; and second, as the fraction calculated relative to the available sites in that phase, denoted as Π f . In this situation, the second phase effectively acts as an excluded volume, reducing the number of available sites. At a constant concentration of the excluded-volume phase, increasing the size of this phase causes the percolation threshold to first decrease and then converge to a constant value. The constant value corresponds to a state in which the structure of conductive sites within the available volume is similar to that of a homogeneous system. In this case, the percolation threshold expressed relative to the available sites is given by Π f = Π homogen , which equals 0.31 in the case of a simple cubic lattice; additionally, the percolation threshold relative to all sites is given by Π = (1 − φ A )Π homogen , where φ A is the fraction of the excluded-volume phase. We also studied situations in which particles are distributed between the two phases with different probabilities. In such cases, the percolation threshold lies between the two extreme cases: a fully homogeneous system and a fully segregated system in which one phase acts as an excluded volume.

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