On the critical conductive filler loading in antistatic composites

Conductive particulate inclusions in a continuous insulating matrix typically impart a precipitous drop in electric resistivity commencing at a threshold volume fraction φcrit which depends on filler particle form and spatial distribution. An illuminating formulation relating threshold composition to the morphology of particles having density ρ is φcrit=1/(1+4ρν), where ν is the readily measurable specific void space in a random dense−packed bed of the (powder) filler. Use of this simple expression permits the first satisfactory semiquantitative rationalization not only of most data obtained recently for model systems comprised of polymer−embedded metal spheres, but also of known behavior of rubbers containing carbon blacks having varied complicated sintered−aggregate (aspherical) morphologies.