BOUNDS ON THE COMPLEX PERMITTIVITY OF MATRIX-PARTICLE COMPOSITES

The complex effective dielectric constant epsilon of matrix-particle composites is considered. Such composites consist of separated inclusi ons of material of type one embedded in a matrix of material of type t wo. The analytic continuation method is used to derive a series of bou nds which incorporate a nonpercolation assumption about the inclusions . The key step in obtaining these improved bounds is to observe that t he nonpercolation assumption restricts the support of the measure in t he integral representation for epsilon (O. Bruno, Proc. R. Sec. Londo n A 433, 353 (1991)). The further the separation of the inclusions, th e tighter the restriction on the support. The new bounds are applied t o sea ice, which is assumed to consist of a pure ice matrix with rando m brine inclusions. Using experimental measurements of the average siz e and separation of the brine pockets, end points of the support of th e 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 an d Hashin-Shtrikman bounds. (C) 1995 American Institute of Physics.