Pressure dependence of the electrical transport in granular materials

We report on systematic measurements of the electrical resistance of one- and three-dimensional (1D and 3D) metallic and oxidized granular materials under uni-axial compression. Whatever the dimension of the packing, the resistance follows a power law versus the pressure (R proportional to P-alpha), with an exponent much larger than the ones expected either with elastic or plastic contact between the grains. A simple model based on a statistical description of the micro-contacts between two grains is proposed. It shows that the strong dependence of the resistance on the pressure applied to the granular media is a consequence of large variabilities and heterogeneities present at the contact surface between two grains. Then, the effect of the three-dimensional structure of the packing is investigated using a renormalization process. This allows to reconcile two extreme approaches of a 3D lattice of widely distributed resistances: the effective medium and the percolation theories.