We report a study of the electrical behavior of metallic beads' assemblies and show how those behaviors are related to the Branly effect. Indeed, as first evidenced by Branly in the late 19th century, a fine metallic powder undergoes a ‘transition' from an insulating to a conductive state driven by the current crossing it. The mechanism of such an electrical instability is still actively investigated. The main features of Branly effect consist of that resistive transition and the current-voltage characteristics reported in systems as simple as pairs of beads as well as larger beads assemblies. The low current ohmic I-V characteristic is associated with a very high linear resistance RL. At higher current, nonlinear effects lead to a ‘flattening' of the upwards characteristic, with a systematic trend to voltage saturation. The backward I-V characteristic exhibits a clear hysteretic behavior and a modified ohmic regime associated with a strongly reduced resistance.

Though not fully understood, it is believed that the non-linearity of the I-V characteristic and the saturation effect arise from enhanced thermal effects resulting in a local melting of the beads' material within the mechanical contact area. However, due to persistent grey areas regarding our poor knowledge about electrical and thermal transfer through multi-contacts interfaces, these micro-contacts nucleation alone cannot account for the whole voltage-current characteristics. The melting effect requires high local heating made possible by Holm's like constriction effects. However, the corresponding surface melting temperatures are too high to be reached at moderate current and there is no experimental evidence for such values. But this argument cannot discard this possibility which can be hidden by the high thermal conductivity of metals. In fact, the melting hypothesis proceeds from the way usually followed to assess the temperature increase at the interface: it relies on the Wiedemann-Franz law and a more questionable assumption regarding the heat transfer along current streamlines. This last assumption appears to be valid only at large distances from the interface. This raises the issue of electro-thermal coupling at metallic interfaces under mechanical load, or more generally, the crucial need for a physical model accounting properly for the Branly effect.

A process which could reduce efficiently the interface resistance is electron tunneling. In situations involving two (at least) metallic solids tightly compressed, tunneling is certainly active. The influence of additional non classical ingredients, such as quantum tunneling should be investigated more deeply. Consequently, a tentative model of electron transport through a system of contacting beads influenced by mechanical stresses and electron tunneling is presented. The usually observed hysteretic features and the slow relaxation of the electrical properties of the whole assembly are obtained. The model emphasizes the competition between two major ingredients: the electron tunneling through the insulating oxide layer and the local melting effect previously stated. Considering the single contact between two adjacent beads as a simple parallel RC circuit with a capacitive element accounting for the dielectric properties of the insulating layer, the model is ruled by a kinetic equation based on quantum tunneling.

Solving this equation with a homemade numerical code developed on Matlab, we computed the corresponding I-V characteristics and reproduce their observed typical shape (hysteresis loop). The model accounts properly for both the nonlinear nature of the characteristic as well as the hysteretic loop. Additional predictions regarding the influence of the mechanical conditions imposed to the interface are discussed. This work may open the way to the modeling of the electrical transport in many beads system to be associated with more complex electrical networks. Higher complexity systems can be easily handled by using appropriate probability distributions.