Polarizability of microemulsion droplets

Spheroidal fluid droplets immersed in another fluid and thermally fluctuating in the shape are considered. The polarizability of the droplet is evaluated up to the second order in the fluctuation amplitudes and also the previous first-order calculations from the literature are corrected. The correlation functions of the polarizability tensor components are found and used to describe the polarized and depolarized scattering of light, and the Kerr effect on microemulsions in the limit of small concentration of the droplets. An alternative simple derivation of the Kerr constant is also given assuming that the droplet in a weak electric field becomes a prolate ellipsoid. We consider both the case when the thickness of the surface layer is neglected and when the droplet is covered by a layer of nonzero thickness. The result differs significantly from that used in the literature to describe the Kerr-effect measurements on droplet microemulsions. Due to the difference the bending rigidity constant of the layer should be increased about two times in comparison with the value found in the original experiments.