The electrical conductivity of a composite model system formed by highly structured carbon black (CB) filled, within an amorphous polymer, poly(ethylene terephtalate) composite is studied. The dc conductivity as a function of CB content follows a scaling law of the type $\sigma \propto (p-p_c{)}^t$ yielding for the percolation concentration, $p_c=0.011\mathrm{}$ and for the exponent, $t=2.17\mathrm{}$. The analysis of the temperature dependence of the conductivity suggests that for temperatures larger than 45 K, conduction can be ascribed to thermal fluctuation induced tunneling of the charge carriers through the insulating layer of polymer separating two CB aggregates. At lower temperatures, conductivity becomes temperature independent, which is typical of conventional tunneling. The frequency dependence of the conductivity is also studied between dc and ${10}^9$ Hz. By the introduction of a shift factor $a_p,$ a procedure for the construction of a master curve based on a “time-length equivalence principle” is proposed. Finally, a model is introduced to describe the frequency dependence of the conductivity of CB-filled composites based on the behavior of charge carriers placed in a fractal object.

• Received 7 March 1997

DOI:https://doi.org/10.1103/PhysRevB.57.2286