Some aspects of electrical conduction in granular systems of various dimensions

TL;DR

This study investigates electrical conduction in 2D and 1D granular systems, revealing logarithmic voltage increase at low currents, saturation due to microcontact welding, and localized current paths in 2D lattices.

Contribution

It provides new insights into the conduction mechanisms and microcontact welding effects in granular systems of different dimensions, including a novel current path mapping technique.

Findings

Voltage increases logarithmically at low currents

Saturation occurs due to microcontact welding

Current paths are localized in discrete linear paths

Abstract

We report on measurements of the electrical conductivity in both a 2D triangular lattice of metallic beads and in a chain of beads. The voltage/current characteristics are qualitatively similar in both experiments. At low applied current, the voltage is found to increase logarithmically in a good agreement with a model of widely distributed resistances in series. At high enough current, the voltage saturates due to the local welding of microcontacts between beads. The frequency dependence of the saturation voltage gives an estimate of the size of these welded microcontacts. The DC value of the saturation voltage (~ 0.4 V per contact) gives an indirect measure of the number of welded contact carrying the current within the 2D lattice. Also, a new measurement technique provides a map of the current paths within the 2D lattice of beads. For an isotropic compression of the 2D granular medium, the current paths are localized in few discrete linear paths. This quasi-onedimensional nature of the electrical conductivity thus explains the similarity between the characteristics in the 1D and 2D systems.