SUPERLOCALIZATION OF THE ELECTRONIC WAVE-FUNCTIONS IN CONDUCTIVE POLYMER BLENDS AT CONCENTRATIONS NEAR THE PERCOLATION-THRESHOLD

The ability to solution-process polyaniline (PANI) in the protonated conducting form through the use of surfactant counterions has enabled the fabrication of conductive polymer blends with a percolation threshold at a volume fraction near 1 %. Electron micrographs of blends of PANI complexed with camphorsulfonic acid (CSA) in poly(methyl methacrylate) show a tenuous interconnected network; for concentrations of PANI-CSA near the percolation threshold, the network is self-similar. Digital analysis of the micrographs shows that in thin two-dimensional 'slices' the PANI-CSA networks are fractal, with the area (S) of the conducting network varying as S is-proportional-to r(D), where D < 2 for concentrations below 4 %. Near the threshold, we find D almost-equal-to 1.5, implying a fractal dimensionality in three dimensions of ca. 2.5. The electrical conductivity of these blends follows the Mott-Deutscher model for variable-range hopping on a fractal network, sigma(T) approximately exp[-(T0/T)gamma]. We find that gamma increases from gamma = 1/4 in pure PANI-CSA (indicting variable-range hopping among exponentially localized states) to gamma almost-equal-to 2/3 as the PANI-CSA concentration is reduced to the percolation threshold, indicating variable-range hopping among superlocalized states on the fractal structure in the limit where the Coulomb interaction between the electron and the hole dominates the intersite hopping.