Evaluation of Dielectric Mixing Models for the Relative Permittivity of Epoxy/Barium Hexaferrite (BaO·6Fe₂O₃) Particulate Composites

Dispersion-filled polymer composites allow the dielectric response of an insulating matrix to be tailored through the type, size and loading of an embedded second phase. In the present work, the relative permittivity of a two-phase system, consisting of an ED-20 epoxy matrix (ε₁ = 3) filled with micron-sized barium hexaferrite (BaO·6Fe₂O₃, ε₂ = 15, effective density 5200 kg·m^？3) particles, was studied as a function of filler content and particle size. Composites with spherical filler particles of diameter 2 μm and 20 μm were measured at filler fractions of 0%, 20%, 40% and 60%. Seven classical effective-medium and mixing relations, the Maxwell-Garnett, Lichtenecker, Wagner, Birchak (square-root), Hashin-Shtrikman, Spichnyak-Novikov and Lorentz-Lorenz models—were compiled and evaluated against the data. The effective permittivity increased monotonically with filler content, from 3 for the neat resin up to 9.2 (2 μm) and 5.2 (20 μm) at 60% loading. The fine-particle system is described well by the square-root mixing rule, whereas the coarse-particle system falls below all classical isotropic predictions, indicating a pronounced particle-size (interfacial-area) contribution that the classical size-independent rules do not capture.