Evaluation of a rigorous lower bound for the intrinsic conductivity of dispersed particles in composites with unknown microstructure

In this theoretical and experimental work we present a novel method to evaluate a rigorous lower bound for the conductivity of a constituent in a binary material, ?min????p, by inverting its measured effective permittivity. A key feature of the procedure is that it applies to heterogeneous systems of arbitrary?and possibly unknown?isotropic or anisotropic microstructure (composites, mixtures, filled porous materials etc). In many cases the simple analytical formula we derive even yields the correct conductivity or at least a good approximation: the more homogeneous the field distribution in the conductive phase is the closer the values ?p and ?min are. The only input that is required is the volume concentration as well as the low frequency part of the dielectric spectra, i.e. of both the binary material and of the less conductive second constituent (the matrix material). The method can be used, e.g. to investigate dispersed nano-particles of any shape, orientation and spatial distribution, the intrinsic properties of which can deviate from bulk values either due to changes during sample preparation or due to possible size or surface effects.