Direct Imaging of the Percolation Network in a Three-Dimensional Disordered Conductor-Insulator Composite

We have directly imaged the percolation network at the surface of a three-dimensional carbon-black-polymer composite using an electric force microscope. At intermediate length scales the conductive area exposed at the surface increases with surface area according to a power law corresponding to a three-dimensional infinite cluster of fractal dimension $D=2.6\mathrm{}\pm 0.1$. This value is in good agreement with the scaling theory prediction, $D=2.53\mathrm{}$. At large length scales the behavior is homogenous with the classical exponent $D=3\mathrm{}$.