The Kerr constant of a microemulsion for a low volume fraction of water

A theoretical analysis of the Kerr effect of an oil continuous water/AOT/isooctane microemulsion in the limit of a low volume fraction of water is given. The microemulsion consists of small nanometer sized waterdroplets, covered by a monomolecular layer of AOT. In the absence of a constant electric field these droplets are spherical. Because of the field their shape changes and becomes, if the field is not too strong, spheroidal. The eccentricity of the spheroids is found by minimizing the total energy of deformation which is a sum of an electromagnetic contribution and a contribution due to the curvature-dependent energy of the droplet surface. The Kerr constant per droplet is then found by deriving explicit expressions for the optical and dielectric polarizabilities along and orthogonal to the symmetry axis of the spheroid. We find that the negative birefringence for small radii of the droplets is a consequence of the optical anisotropy of the AOT molecules, which are all “lined up” orthogonal to the water surface.