Superlocalization of the electronic wave functions in conductive polymer blends at concentrations near the percolation threshold

Abstract

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 concentration 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 {alpha} r{sup D}, where D < 2 for concentrations below 4%. Near the threshold, they find D {approximately} 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[{minus}(T{sub 0}/T){sup {gamma}}]. They find that {gamma} increases from {gamma} = 1/4 in pure PANI-CSA (indicting variable-range hopping among exponentially localized states) to {gamma} {approximately} 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 holemore » dominates the intersite hopping.« less