Stress-dependent frequency response of conductive granular materials

Electrical networks of randomly distributed resistors, capacitors, and inductors have been observed to exhibit intrinsic electrical characteristics that show power law behavior with respect to the frequency of the electrical signal applied. To examine these scaling laws, we present an experimental investigation of the stress-dependent electrical properties of randomly packed spheres of stainless steel, subjected to various conditions of compressive force. We considered two types of spheres exhibiting different dimensions, in order to have different inter-particle forces, which govern interfacial electrical properties, at a given stress. The frequency-dependent conductance and impedance of packed beds are found to demonstrate power-law relationships within a certain range of frequency. The absolute value of the exponent of the observed power function varies with the applied stress. The capacitive-to-inductive phase transition was observed as load increased, and was found to depend on the applied stress level and surface-to-volume ratio. The approach of equivalent network circuit was developed to describe the variation of macroscopic impedance at various frequencies. This study provides an insight into the characteristic electrical behaviors of conductive granular materials.