Nonlinear electrical conductivity in a 1D granular medium

Abstract.We report on observations of the electrical transport within a chain of metallic beads (slightly oxidized) under an applied stress. A transition from an insulating to a conductive state is observed as the applied current is increased. The voltage-current (U-I) characteristics are nonlinear and hysteretic, and saturate to a low voltage per contact (0.4 V). Our 1D experiment allows us to understand phenomena (such as the “Branly effect”) related to this conduction transition by focusing on the nature of the contacts instead of the structure of the granular network. We show that this transition comes from an electro-thermal coupling in the vicinity of the microcontacts between each bead - the current flowing through these contact points generates their local heating which leads to an increase of their contact areas, and thus enhances their conduction. This current-induced temperature rise (up to 1050 $^{\circ}$C) results in the microsoldering of the contact points (even for voltages as low as 0.4 V). Based on this self-regulated temperature mechanism, an analytical expression for the nonlinear U-I back trajectory is derived, and is found to be in very good agreement with the experiments. In addition, we can determine the microcontact temperature with no adjustable parameters. Finally, the stress dependence of the resistance is found to be strongly non-hertzian due to the presence of the surface films. This dependence cannot be usually distinguished from the one due to the disorder of the granular contact network in 2D or 3D experiments.

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