The dual-arc impedance behavior of short conductive fiber composites can be rationalized on the basis of the model pictured in Fig. 2. This model is based on recent work with single and multiple fibers (steel, copper) suspended in a low conductivity medium (tap water) and measured or modeled for impedance response along the axis of the fibers [27]. The unique frequency-dependent behavior arises due to highly resistive "coatings" on the conductive fibers. In the case of steel, these may or may not include a passive oxide film. In all cases, however, a polarization layer (double layer/charge transfer resistance) forms at the fiber:electrolyte interface. Under DC and low frequency AC excitation, these layers act to make the fibers insulating, so that their effect on overall electrical transport through the composite is negligible. In terms of the equivalent circuit in Fig. 2b, the bottom path is open and the current flow (dashed line in Fig. 2a) is unperturbed from the no-fiber situation. As frequency increases, however, the "coating" impedance goes to zero, causing the fibers to act as short-circuits in the composite. The "switch" is closed on the lower path in Fig. 2b, which becomes increasingly important in overall transport. The result is the subdivision of the single Nyquist arc, in the case with no fibers, into two separate arcs. The diameter of the high frequency arc is given by the difference between the resistance of a composite with insulating fibers (low frequency) and the resistance of a composite with highly conducting fibers (intermediate frequency). When the fibers are highly conducting, the composite resistance is a combination of matrix resistance (between fibers and between fibers and the electrodes) and spreading resistance due to current-bunching at the fiber tips (i.e., the solid current lines in Fig. 2a). The current constriction at intermediate frequencies was confirmed by grey-scale images of current density in pixel-based computer calculations [27]. Some amount of current constriction occurs for any shape of highly-conducting inclusion, including spherical inclusions [27], but is greatest for inclusions that are long and thin in the direction of the applied field [1,27].
Fig. 2. Schematic diagrams of a) current flow and the b) equivalent circuit for the frequency-switchable fiber coating model. At DC and low AC frequencies, the fiber "coating" (double layer impedance and/or oxide film) is insulating and the bottom path is "open" in b); the current flow in a), the dashed lines, is as if the fiber were not present (R b, Cb; b = bulk). By intermediate frequencies, however, the coating impedance is eliminated and the "switch" is thrown in the lower path of b), which now dominates current flow in a), the solid lines. In the bottom path, " bo" stands for the outer bulk regions, and "sp" stands for the spreading resistance/capacitance associated with the current-bunching (spreading resistance) zones at the fiber tips.
Although the basic features of the impedance response of short conductive fiber composites (relative insensitivity of the DC resistance to the presence of fibers and subdivision of the bulk impedance arc into two arcs) have been qualitatively explained, quantitative relationships between experimental parameters such as RCUSP (or γ) and composite microstructure must be developed. The present study investigated the roles of fiber pull-out, fiber debonding, and fiber orientation on the impedance response of conductive fiber composites. As in our prior study [27], a combination of physical simulation (fibers in tap water) and pixel-based computer modeling was employed, to compare and contrast with actual composite behavior.