Topological Features of Conductive Network Formation in Metal–Polymer Composites with Varying Filler Particle Sizes

The topology of the infinite cluster in polymer composites containing micro- and nanoparticles of Ni was investigated, enabling a quantitative evaluation of how the size of conducting particles influences the percolation transition and the structure of the conductive network. The use of nanosized Ni reduces the critical concentration to Vs ≈ 0.105, compared with Vs ≈ 0.21 for microparticles, increases the parameter σ₁ by more than an order of magnitude, and results in a sharper, more localized percolation transition. The cluster structure exhibits pronounced fractal–hierarchical features: the fractal dimension of the backbone is 1.6-1.8 and that of the dangling ends is 1.9-2.1. The cluster density, correlation radius, and topological parameters follow power-law relations typical of three-dimensional percolation (ν = 0.85). At high concentrations of the conducting phase (V ≥ 0.3), the asymptotic conductivity reaches 63 Ω⁻¹·cm⁻¹ in nanocomposites versus 8 Ω⁻¹·cm⁻¹for microparticle-based materials. These findings confirm the high efficiency of Ni nanoparticles in forming an extended, interconnected, and branched conductive network, providing the foundation for next-generation high-conductivity composites.

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