The effective dielectric constant of a dispersion of spheres

Dielectric properties of a dispersion of spheres in a background medium are studied. First the many-body electrostatic interaction problem is solved by an expansion in irreducibles tensors. The effective dielectric constant εe of the system is then calculated using a fluctuation expansion. The theory is not restricted to low concentrations and/or low polarizabilities, nor to dipole interactions. The lowest order of the fluctuation expansion, which is evaluated for all wavelengths, reduces in the infinite wavelength limit to the familiar Clausius-Mossotti result εCM. Calculations of the next non-vanishing order requires knowledge of the pair correlation for the spheres, which we describe by the Percus-Yevick function corresponding to a hard-sphere fluid. It is shown (1) that higher order multipoles account for 50% of the calculated correction to εCM, (2) that the conjecture of Stell and Rushbrooke, stating that contributions from the third and higher powers of the polarizability to the quantity S of the Kirkwood-Yvon theory are negligible, is justified. The influence of an algebraic resummation of self-correlations on the fluctuation expansion is studied. The results of the theory are compared to those of other theories and to experimental data.