Electrical conductivity of a mixture of conducting and insulating spheres: an application of some percolation concepts

An extensive study of a large, compact, disordered ensemble of plastic spheres of constant diameter, a fraction p of which has been metallically coated is reported. An initial discussion deals with the compactness and average connectivity z of the system. The electrical conductance for completely conducting samples (p=1) has been studied as a function of pressure applied uniaxially to the ends of a cylindrical container, and compared to that of individual contacts in test samples. Although the variation of conductivity with p is consistent with expectations for a site percolation problem, the idea of a simultaneous bond percolation must be introduced to take into account variations in the quality of the different contacts.