For some years, several authors have tried to explain the behavior of elect
ric field induced birefringence in some microemulsion systems. In this work
we continue a line based on works by van der Linden [S. Geiger, E. van der
Linden, D. Bedeaux, Physica A 156(1989) 130, C. Roman Vas, G.J.M. Koper, E
. van der Linden, J. Phys. II(France) 4 (1994) 163] and others, using a mat
hematical description derived from first principles without approximations.
Previous work assumes that the AOT layer width is small compared with the
radius of the core, and that the static permittivity of the core-water in w
ater in oil (W/O) microemulsion is practically infinite. These assumptions
are questionable for small droplets where negative birefringence is observe
d, and also for O/W microemulsions. Our model sets no restriction on the la
yer width or the core static permittivity, yielding general analytical equa
tions for the calculation of the Kerr constant. Nevertheless, for two exper
imental systems, our conclusions are essentially in agreement with these au
thors, while discrepancies in the numerical values of the relevant paramete
rs have been observed. Namely, larger values for the rigidity elastic const
ant have been found, results compatible with previous theoretical predictio
ns arising from general principles and experimental works. (C) 1999 Elsevie
r Science B.V. All rights reserved.