The conductivity of composites with a carbon fiber (CF) content slightly higher than the percolation threshold was measured at increasing temperatures up to À10 1C. The tunneling effect was theoretically calculated using a rigorous nonparabolic potential barrier. The tunneling barrier width D and the surface area A were determined. For a polyethylene (PE) matrix, good agreement between theoretical and experimental results was obtained using D ¼ 1.00 nm and A ¼ 1.35 to 1.68 nm 2 at a 30-vol% CF content and using D ¼ 1.30 nm and A ¼ 1.25 to 1.28 nm 2 at a 25-vol% CF content. That is, almost perfect agreement between experiment and theory was obtained by adjusting the parameters except over the temperature ranges in which the b and c relaxation peaks appeared. Dynamic loss modulus and positron annihilation measurements were also conducted. However, a theoretical analysis that was derived using a parabolic potential barrier produced inconsistent results. That is, the tunneling barrier width D was less than the c-axis length of a PE crystal unit, and the surface area A was considerably less than the a-b plane area of a PE crystal unit.
INTRODUCTIONIt is well-known that the conductivity of composite systems, such as polymer-carbon nanotube composites, polymer-carbon fiber (CF) composites, and polymer-carbon black composites, increases with temperature up to 0 1C and then decreases upon further increasing the temperature. 1-12 The conductivity increase up to 0 1C by the enhancement of electron transport has been attributed to two mechanisms, electron hopping 13-17 and electron tunneling. [2][3][4][5][18][19][20][21][22] Electron hopping is thought to occur by two mechanisms. The first mechanism predominates at high temperatures at which there is sufficient excess thermal energy to excite the electrons into the conduction band, and the conductivity can be evaluated using Arrhenius plots. The second mechanism is known as variable range hopping (VRH) and has been theoretically modeled by Mott and Davis 13 at low temperatures, the excited electrons lose their ability to jump into the conduction band and instead attempt to find a state with similar energy to their own by hopping beyond their nearest neighbors to more distant sites, corresponding to a greater selection of possible electron energy levels.Two types of electron tunneling have been observed. The first type is the electric tunneling effect, which occurs between similar