Experimental observation of nonuniversal behavior of the conductivity exponent for three-dimensional continuum percolation systems.

Abstract

We measured the conductivity of both silver-coated-glass--Teflon composites and indium-glass composites made with use of standard mixing and pressing techniques. In the conducting-sphere--insulator composites, the silver-coated glass spheres were randomly distributed inside the Teflon host, with the conduction occurring only through the contact point between spheres. For this composite, we found t=2.0\ifmmode\pm\else\textpm\fi{}0.2 and ${p}_{c}$=0.170\ifmmode\pm\else\textpm\fi{}0.002, in agreement with the conventionally accepted values of t and ${p}_{c}$ for a three-dimensional (3D) random composite. In the insulating-sphere--conductor composites, the hard glass spheres were randomly distributed inside the indium. For these composites, we found the percolation threshold to be strongly dependent upon the pressure used to make the sample, with ${p}_{c}$ usually falling between 0.04 and 0.1, well below the expected value for a 3D random composite. Scanning-electron-microscope pictures show that narrow necks of the conducting paths do exist. The conductivity exponent was independent of the pressure used to make the sample and equal to t=3.1\ifmmode\pm\else\textpm\fi{}0.3. The difference between the above two exponents shows that the conductivity exponent for continuum percolation systems in 3D is not universal.