The effect of the interface on the dc transport properties of nonlinear composite materials

The effects of the interface separating two strongly nonlinear electric conductors is investigated. The interface may either be highly conducting or exhibit an electric contact resistance. Our analysis and results are based upon new variational principles for nonlinear composites with surface energies. For monodisperse suspensions of spheres separated from the matrix by a highly conducting interface, a critical direct-current ~dc! applied field strength is found for which the electric potential inside the sample is the same as for a sample containing no spheres. For this field strength the overall electric current passing through the sample is the same as for a sample containing pure matrix conductor. When there is a contact resistance between the matrix and sphere phase, a critical dc applied current density is found for which the current density inside the sample is the same as for a sample containing no spheres. These results are shown to be independent of the location of the spheres within the sample. Moreover, this effect is independent of the concentration of spheres in the sample even beyond the onset of interface percolation. © 1999 American Institute of Physics. @S0021-8979~99!06315-X#