An Equivalent Circuit Approach to Evaluating Conductivity of Polymer-Filler Composites
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An Equivalent Circuit Approach to Evaluating Conductivity of Polymer-Filler Composites Vladislav Skorokhod Xerox Research Centre of Canada 2660 Speakman Drive Mississauga, Ontario L5K 2L1, Canada ABSTRACT An equivalent circuit model of electrical conduction in polymer-filler particulate composites was developed in this study. The equivalent circuit was constructed for an individual composite particle with a sub-monolayer of conductive filler, where the filler particles play the role of circuit nodes, and inter-particle contacts are represented by resistors between the nodes. The mathematical representation of the equivalent circuit in the form of a linear system of equations for nodal potentials was solved numerically with Matlab software to calculate conductance of the composite as a function of the amount of conductive filler, filled fraction of the monolayer, filler-to-matrix size ratio and the degree of structuredness (non-randomness) of the filler material. Additionally, percolation concentrations and statistical distributions of composite conductance were calculated as functions of the filler-to-matrix size ratio. INTRODUCTION Conductive mixtures of polymers and conductive fillers (such as carbon black, elemental metal or metal oxide powders) find a variety of technological applications, such as antistatic materials, and materials for electromagnetic shielding. Electrical properties of conductive polymer composites are often required to be fine-tuned to meet certain specifications, which demands good understanding of the electrical conduction mechanisms in such composites. Typically, electrical conductivity of polymer-filler composites increases rapidly at the percolation concentration of the filler, and then continues to increase further with filler content in an exponential manner. Comprehensive reviews on various composite configurations and various approaches in percolation theory and can be found in literature [1, 2]. Geometrical percolation models [3, 4, 5] describe and give good approximations for the percolation effect in particulate composites comprised of insulative particles with surface layers of fine conductive additives. These studies consider the conductive surface layer to be a relatively thick multi-layer of fine particles, however, they do not address the case when the filler particles form a monolayer or a sub-monolayer as for example in the case of xerographic toner particles with surface additives. Also, the previous literature on geometrical percolation models focus on the bulk conductive properties of conductive composites in a compacted form rather than in the form of individual composite particle or loosely packed powder. The present study addresses several important aspects of electrical conduction of matrix-filler particulate composites, expanding on work in previous studies. This new work here can be of great interest for certain conductive composite applications, including the method to estimate conductance of an individual composite particle with a monolayer or sub-monola
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