Percolation properties of cellular composite systems
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Percolation properties of cellular composite systems C. Chiteme and D.S. McLachlan School of Physics and Material Physics Institute, University of the Witwatersrand, Private Bag 3, Wits 2050, Johannesburg, South Africa. Percolation phenomena were studied in a series of six composites with a cellular structure. Measurements made on the composites include dc and ac electrical conductivity, dielectric constant, 1/f or flicker noise and magnetoresistance. Results arising from these extensive measurements were fitted to the percolation power laws and a phenomenological equation to give various exponents, which are presented, discussed and compared. INTRODUCTION This paper is to some extent a sequel to the previous paper, in that it will go into detail regarding the percolation parameters observed in a new and very extensive set of measurements made on cellular percolation systems. Cellular systems [1,2,3] are ones where large diameter (2Ri) grains (in this case~ 300µm) are covered with a much smaller diameter (2Rc) conducting powder (with mean diameters in the range 3-35µm). Kusy [4] has proposed a model for such systems, which have very low values of the critical volume fraction φc [1]. Note that the conducting powders on the surfaces of the grains consist of Links (a single current carrying element between two nodes), Nodes (a point where three or more links meet) and Blobs (regions where the current flows in parallel in conducting elements or “wires” between links and nodes) [5,6]. In addition to the LBN structure, there are dead end elements and clusters of conducting elements where no dc current flows. EXPERIMENTAL RESULTS AND DISCUSSION The preparation of and the dc and ac measurements are described in detail in [1,2]. The equations used to analyze the data have been given in the previous paper [7], as has some illustrative data on some of these cellular systems and the granular Graphite-Boron Nitride system [8,9]. The parameters obtained are given in Table I. It is important to note that the Kusy model is for spherical particles with a single value for Ri and Rc. The actual particles used had a range of sizes and only the Ground and Raw Carbon Black (GCB and RCB), Niobium Carbide and Fe3O4 can be considered to be reasonably spherical. However, only the GCB and Fe3O4 results are in good agreement [1] with the Kusy [4] model. The Graphite and Graphite-Boron Nitride powders are in the form of flakes. Note that Niobium Carbide and Fe3O4 powders are granular with some pointed facets. As can be seen from Table I, the t values for GCB and GG are close to the universal value of 2.0, the values for RCB and GBN are somewhat higher and those for the faceted grains, Fe3O4 and NbC, are much larger than tun. Kogut and Straley [10] showed that if the low conductance bonds in the percolation network (computer simulations) or experimental system had a very wide distribution then t could be larger than tun =2. This distribution can be due to a large range of effective geometrical factors in a continuous homogeneous conducting media
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