Percolation via Electrical Conduction

Mateo Chinchilla

2008

An experiment was conducted to study the ideas pertaining to percolation by observing the flow of electricity through a system of conducting and insulating spheres. Determinations of the percolation threshold pc were achieved by measuring the resistance of the system. Preliminary investigations were conducted to determine the effects of pressure, sphere organization and system settling on the resistance. The bulk of the experiment concentrated on measuring the percolation threshold of three different size systems by varying the number fraction of conducting spheres in the mixture of ~3 mm in diameter steel shot and glass spheres. Results have qualitative and quantitative similarities to published work done on comparable systems, both experimental and through simulations. A hyperbolic tangent function was used to extract the percolation threshold and steepness of the curve at the percolation threshold. The percolation threshold value obtained in the 15-layer system is pc = 0.719 and pc = 0.87 in the 4-layer system. A shift in the percolation threshold consistent with 2D to 3D modeling was observed as the system size increased. The varying system size also influenced the steepness of the curve. Using the work of Khanikaev et al, the small difference in sphere size between conducting and insulating spheres was determined to have a negligible effect on pc. Finally, mean-field theories and a fit function proposed by Brouers were used to investigate bead geometry under pressure. The hyperbolic tangent function described the data better than the Brouers' function. It was concluded, from the experimental data collected and its comparison to theoretical values, that the percolation threshold observed is not representative of bond or site percolation, but rather a mixture of the two.