Percolative and Conductive Properties of Spherical Mixtures

Mark Zimmerman


The electrical conduction of a cylinder filled with silver-coated glass spheres (d = 1:064 �0:006 mm) and uncoated glass spheres (d = 1:00 � 0:01 mm) was investigated using percolation concepts. At high fractions of silver-coated spheres, the system conducts electricity, but, at low fractions, the system is insulating. Between these two extremes, the behavior switches between insulating and conducting phases at a critical point called the percolation threshold; this study has located this critical point at a volume fraction of 0:21 �0:02. Our value is consistent with those for similar systems reported in the literature. The impact of system size on the percolation threshold and also the conductance was investigated, and the height of the system was observed to have an effect. As the height of the system decreased, either the percolation threshold occurred at a lower volume fraction or the conductance increased more quickly. The normalized conductance was not observed to vary as the width of the cylinder was changed, but the overall conductance was observed to increase as the width increased. Finally, the conductance above the percolation threshold was observed to be consistent with a second order power law as expected from the literature, and the coefficient was found to be proportional to area/height.