Percolation in disordered conductor/insulator composites

Disordered insulator/conductor composites, which are composed of conducting particles randomly distributed in an insulator matrix, has been studied for decades. They are promising materials in various fields such as electrodes for lithium ion batteries and solid oxide fuel cells, inert anode materials for Al production, solar energy conversion, anti-corrosion coating under marine environment, electrical devices, sensors, catalysts, and supercapacitors. The properties of disordered insulator/conductor composites show advantages because of combining the merits from the insulating matrix and conducting fillers. The widely investigated disordered insulator/conductor composites are carbon/polymer composites, carbon/ceramics composites, or metal/ceramic (cermet) composites, in which the insulating matrix is a polymer or ceramics while the conductors are metals, or carbon materials, including carbon black (CB), graphite, carbon fibers (CF), carbon nanofibers (CNF), carbon nanotubes (CNT), or graphene (GR). The critical behavior, as a specific phenomenon of the disordered insulator/conductor composites, is governed by the geometrical structure and dispersion condition of the conductors in the insulator matrix, and in most cases, it also decides the overall properties of the composites. Percolation, the main theory explaining the critical transport phenomenon of disordered materials, was widely studied in the past decades. The investigation of the shortest path, tortuosity, fractal characterization of the conducting phase, percolation threshold, critical exponents, elastic constants, and fluid permeability are the top challenges in this filed. In this chapter, the percolation phenomenon of the disordered insulator/ conductor composites, including carbon/polymer composites, carbon/ceramics composites, and metal/ceramic composites, are systematically introduced. The shortest path, tortuosity, fractal characterization, and percolation backbone density of the conducting phase are discussed. Meanwhile, the percolation threshold, the critical exponents based on the electrical conductivity, and the mechanical and thermal properties near the percolation threshold are also analyzed. This chapter can be used as a reference for the materials scientists as well as physicists who are working on the percolation phenomenon of the insulator/conductor composites.