Fractal Analysis of Disordered Conductor–Insulator Composites with Different Conductor Backbone Structures near Percolation Threshold

To obtain a different backbone structure of conductors in disordered insulator/conductor composites, Cu 2 O/Cu composites were prepared using two methods, named the direct hot-pressing (DHP) method and the in-situ reduction hot-pressing (IRHP) method via hot-pressing Cu 2 O powders and branch-like or spherical Cu powders and hot-pressing Cu 2 O powders and carbon black (CB) nanoparticles to reduce Cu 2 O into Cu, respectively. The dc electrical conductivity tests show that the percolation threshold of the prepared Cu 2 O/Cu composites varies with various Cu structures. The lowest and the highest percolation thresholds were obtained in those with branch-like Cu and with CB nanoparticle-reduced Cu, respectively. The percolation structures of Cu were analyzed by fractal theory, and the binarized optical microscope images were used for the box-counting fractal dimension calculation. Near the percolation threshold, the fractal dimension increases with an increasing volume fraction of Cu in all prepared Cu 2 O/Cu composites. The backbone structure of the conductors was first characterized by the fractal dimension increasing rate with an increasing volume fraction of Cu. For the Cu 2 O/Cu composites prepared with the IRHP method, near the percolation threshold, the fractal dimension increases little with an increasing volume content of Cu; for those prepared with spherical Cu, the rate of increase is relatively higher, and for those prepared with branch-like Cu, the fractal dimension increase rate is the highest.