Electrical conductivity of a mixture of conducting and insulating spheres: an application of some percolation concepts

Abstract

An extensive study of a large, compact, disordered ensemble of plastic spheres of constant diameter, a fraction p of which has been metallically coated is reported. An initial discussion deals with the compactness and average connectivity z of the system. The electrical conductance for completely conducting samples (p=1) has been studied as a function of pressure applied uniaxially to the ends of a cylindrical container, and compared to that of individual contacts in test samples. Although the variation of conductivity with p is consistent with expectations for a site percolation problem, the idea of a simultaneous bond percolation must be introduced to take into account variations in the quality of the different contacts.

Evolution of Davidson–Cole relaxation behavior in random conductor–insulator composites

“…A curve fit, shown in Fig. 12͑b͒, of dc vs p revealed dc ϳ(pϪ p c ) 1.86 , which is in excellent agreement with published results for the conductivity exponent of 1.7Ϯ0.2 and 1.85Ϯ0.25 by experiments of Ottavi et al 63 the example is also consistent with the established numerical value range of 1.85Ϯ0.15, which is based on a variety of simulations available in the literature. 64 The value of p c found from the conductivity fitting was 0.0993, which is very consistent with the 0.1058 value obtained by direct geometrical ''maze solving'' through the network.…”

Experimental determination of magnetocrystalline anisotropy constants and saturation magnetostriction constants of NiZn and NiZnCo ferrites intended to be used for antennas miniaturization

“…Although it might be difficult to theoretically correlate the internal stress σ i with the molding pressure P, the following interpretation allows an understanding of this value of α. The average connectivity (Z) for a compact disordered mixture made of touching hard spheres is [44,45] Z ¼6-7. A pressure P applied onto this structure is transmitted from each sphere to neighboring ones through this irregular lattice.…”

Microstructural Inhomogeneity of Electrical Conductivity in Subcutaneous Fat Tissue

“…It is commonly known that such a system demonstrates a percolating behavior, i.e. by low values of p < p cr its conductivity is zero, by p > p cr conductivity increases with p and it reaches its maximum value at p = 1 [13]. The value of p cr in different percolation systems was assessed to be approximately 0.30.…”