Anomalous electrical conductivity and percolation in carbon nanotube composites

Transport properties of disordered multiphase materials, such as electrical and thermal conductivities, have been an active research area in statistical physics for decades. In a composite consisting of conductive fillers dispersed in an insulating matrix, there is a well-defined insulator– conductor transition when an infinite conductive network or path throughout the matrix is formed. This process can be well described by percolation theory [1, 2]. Recently, carbon nanotube (CNT)-reinforced composites and suspensions have attracted a great deal of attention due to their excellent properties and many potential applications. CNTs have a unique set of mechanical and physical properties, including extremely high Young’s modulus, strength, electrical, and thermal conductivities. The current experiments showed that CNT-reinforced composites exhibit an electrical percolation with addition of 0.1 vol.% or less fillers, at which electrical conductivity rises sharply by several orders of magnitude [3–7]. Here, the percolation threshold of CNTs is closely dependent on their geometric factors (e.g., volume fraction, size, shape, and orientation) and the interaction between them. It is a critical issue in producing conductive composites for use in films, coatings, and paints since the lower percolation threshold can reduce the loading of expensive CNTs, leading to lighter composites. In comparison with composites reinforced with isotropic particles, however, the percolation threshold of composites containing highly anisotropic conductor fillers such as CNTs is still not well understood. The term ‘‘percolation’’ refers to the onset of a sharp transition or an infinite network (or cluster) at which longrange connectivity suddenly appears [1]. The electrical conductivity near the percolation threshold is anomalously greater than that predicted by traditional theoretical models, such as Maxwell, Hamilton-Crosser models [8]. Intuitively, the electrical percolation process in CNT composites is similar to traditional ones with the addition of isotropic conductive particles, but with an ultra-low percolation threshold. As shown in Fig. 1, near the percolation threshold, the probability or fraction of a CNT, P, on the infinite cluster obeys a power law and can be described as P 1⁄2/ /cðaÞ bðaÞ; ð1Þ