Electrical mixing laws for composites with conducting and insulating discs by impedance spectroscopy

Composites made with conducting or insulating discs (right cylinders) in a cementitious matrix were tested by AC impedance spectroscopy. The dual-arc (conducting discs) and single-arc (insulating discs) behaviors were analyzed for conductivity vs. the volume fraction of discs. The resulting mixing laws are in excellent agreement with equations derived from existing mixing laws for the semi-dilute regime, once suitably modified for differences in shape (right cylinders vs. oblate spheroids) and alignment (random vs. aligned). Deviations from random dispersion were readily detected by conductivities in x, y, and z directions, suggesting that AC-IS is sensitive to any anisotropy of discs orientation in such composites. These results are completely general, with potential application for composites involving disc-shaped inclusions (e.g., flakes or cracks).