Temperature dependence of the resistivity in polymer<i>–</i>conducting-carbon-black composites

Abstract

The electrical dc resistivity of variously prepared polymer--conducting-carbon-black composites has been studied over a wide temperature range (4.2--300 K). For the different composites, the resistivity follows a ln\ensuremath{\rho}\ensuremath{\sim}${T}^{\mathrm{\ensuremath{-}}\ensuremath{\alpha}}$ law over the whole temperature range, with the \ensuremath{\alpha} parameter, varying between (1/2\ensuremath{\le}\ensuremath{\alpha}\ensuremath{\le} 3) / 4 , determined by the carbon-black concentration and the dispersion in the carbon grain sizes. The experimental facts can be understood on the basis of a critical-path-method analysis for hopping conduction developed for granular disordered metallic systems.