Fractal analysis of the percolation network in epoxy-polypyrrole composites

The macroscopic dc conductivity and structure of epoxy-polypyrrole composites are studied as a function of the polypyrrole amount and interpreted with percolation concepts. The fractal dimension $D$ of the infinite cluster is found to increase substantially from 1.25 to 1.88 with the conducting filler concentration. An original representation of the conducting backbone is obtained using image analysis techniques and suggests a finitely ramified structure. The Minkowski dimension of the backbone is determined to be an excellent approximation of the fractal dimension $D_B$ and it is seen to increase as the polypyrrole concentration increases while the fractal dimension of the elastic backbone is found to keep the constant value $D_E=1.13\mathrm{}$. These results are compared to scaling percolation theory.