A percolation model of conduction in segregated systems of metallic and insulating materials: application to thick film resistors

Abstract

An expression relating the resistivity, R, of a segregated system of conducting and non-conducting media to the volume fraction, V, of the conducting component has been derived by applying percolation theory to a simple but realistic model of the system microstructure. It is proposed that R varies as (p'-pc)- mu where pc is the percolation threshold, mu is the conductivity critical exponent for 3D systems and p' is the fraction of sites in the conducting region that are filled by conducting particles; p' is related to V. The expression can be used to fit the observed R-V curves (blending curves) of thick film resistor systems, which are known to have a segregated structure. The model is valid over a useful range of volume fractions and employs typical values for pc and mu .

Novel Percolation Mechanism in PMMA Matrix Composites Containing Segregated ITO Nanowire Networks

“…Such a low percolation threshold value is generally characteristic of polymer matrix composites containing segregated network microstructures. [1,2,[9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] The conductivity data also correlates well with the optical transmittance data, which shows a more gradual reduction in the transmittance after 2-3 wt % ITO (Fig. 7).…”

“…[5][6][7][8] Polymer matrix composites containing alternate microstructures may be preferred when lower percolation thresholds are desirable. [1,2,[9][10][11][12][13][14][15][16][17][18][19][20][21][22] Polymer matrix composites are often fabricated with segregated network microstructures in order to reduce the percolation threshold. This microstructure can be developed in two steps: (i) coating the polymer powders with the filler, and (ii) compression molding the mixed powders.…”

“…[1,2,[9][10][11][12][13][14][15][16][17][18][19][20][21][22] After the results published by Turner and co-workers about polymer matrix composites with segregated network microstructures, [9][10][11] several publications have followed describing similar observations. [12][13][14][15][16][17][18][19][20][21][22] Turner et al [9][10][11] proposed that the coating of the filler around the polymer powders was responsible for the percolation seen in segregated network microstructures. It was suggested that the position of the filler remained unchanged once it was applied to the surface of the polymer, which resulted in a segregated network via physical contact between the filler particles after the mixed powders were compacted.…”

“…A high matrix/filler particle size ratio has been found to be necessary in achieving low percolation thresholds and good segregated network microstructures in polymer matrix composites. [1,2,[9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]29] The electrical conductivity of the PMMA/ITO composites as a function of ITO content is shown in Figure 2. The error bars include data from at least three different specimens fabricated under the same conditions.…”

Review of Bi2O3based glasses for electronics and related applications

“…11). 84,463,[468][469][470][471][472][473][474] In classical TFR series, the conductive phase is mainly ruthenium oxide (RuO 2 ) and/or its pyrochlore compounds with PbO and Bi 2 O 3 , lead and bismuth ruthenate (Pb 2 Ru 2 O 72y and Bi 2 Ru 2 O 7 ), and the glassy matrix is a high lead lead borosilicate glass (Fig. 12).…”