Percolation and Tunneling in Composite Materials

Abstract

Classical percolation theory is concerned with the onset of geometrical connectivity and the accompanied onset of electrical connectivity in disordered systems. It was found, however, that in many systems, such as various composites, the geometrical and electrical onsets of the connectivity are not simultaneous and the correlation between them depends on physical processes such as tunneling. The difference between the above two types of systems and the consequences for the electrical transport properties of the latter composites have been largely ignored in the past. The application of scanning local probe microscopies and some recent theoretical developments have enabled a better understanding of the latter systems and their sometimes "strange" behavior as bona fide percolation systems. In this review we consider the above issues and their manifestation in three types of systems: Carbon Black–Polymer composites, metal–insulator cermets and hydrogenated microcrystalline silicon.

Continuum percolation of carbon nanotubes in polymeric and colloidal media

“…Of course, the dependence of on the dielectric constant cannot be very strong because ͉E f ͉ Ͼ Ͼ ͉E e ͉, but because the PT of sticky rods is very sensitive to the value of ⌬, the impact of the polarity of the medium could still be appreciable. For a typical polymer matrix the relative dielectric constant is about 3, giving Ϸ 0.1 nm, consistent with estimates suggesting that the typical distance between two nanotubes should to be less than a nanometer or so to get reasonable conductance (31,35,49). This distance suggests that for SWNTs in a polymer matrix ⌬/D Ϸ 1.1.…”

“…5.) The corresponding local conductivity because of tunneling is ϭ 0 exp [Ϫr/ ], where is the characteristic tunneling distance and 0 some constant (31,46). One way to relate the connectedness percolation theory to electrical percolation is to choose the connectedness criterion ⌬ Ϫ D Ϸ , which would guarantee the underlying percolation network in the polymer composite to be conductive (42,47).…”

Tunneling-percolation origin of nonuniversality: Theory and experiments

“…Nevertheless, the percolation picture ͑with its corresponding critical exponents͒ seems to survive well also in the low-temperature tunneling regime. 61 Hence, a tunneling-percolation theory of piezoresistivity at low temperatures should be formulated by considering percolation networks where the simple tunneling process ͑9͒ are combined with additional terms describing, e.g., grain charging effects and/or Coulomb interactions.…”

Thin film thermistor with positive temperature coefficient of resistance based on phase separated blends of ferroelectric and semiconducting polymers

“…[4][5][6][7][8][9][10] At room temperature the conductive particles form a percolating path and the resistance is low. [11][12][13] When the temperature increases, the large volume expansion of the semi-crystalline polymer close to its melting point breaks up the percolation path and the resistance dramatically increases.…”