Bounds on the complex permittivity of matrix-particle composites

The complex effective dielectric constant E* of matrix-particle composites is considered. Such composites consist of separated inclusions of material of type one embedded in a matrix of material of type two. The analytic continuation method is used to derive a series of bounds which incorporate a nonpercolation assumption about the inclusions. The key step in obtaining these improved bounds is to observe that the nonpercolation assumption restricts the support of the measure in the integral representation for E* (0. Bruno, Proc. R. Soc. London A 433, 353 (1991)). The further the separation of the inclusions, the tighter the restriction on the support. The new bounds are applied to sea ice, which is assumed to consist of a pure ice matrix with random brine inclusions. Using experimental measurements of the average size and separation of the brine pockets, end points of the support of the measure can be determined, and subsequently used to find the allowed range of values of the effective dielectric constant of sea ice. The new bounds are compared with experimental data taken at 4.75 GHz, and exhibit significant improvement over previous fixed volume fraction and Hashin-Shtrikman bounds.