An extensive set of measurements of low-frequency conductivity cr of a three-component microemulsion system, AOT-water-decane, as a function of temperature and volume fraction of the dispersed phase has been made, a can be calculated at low 0 by means of a charge-fluctuation model, while it can be interpreted for higher values of (p in terms of power-law behavior. The percolation locus in the (p-T plane has been determined starting from the vicinity of the lower consolute point up to 0 -0.65. This line can be successfully interpreted in terms of a modified version of the analytical theory of percolation given by Xu and Stell.PACS numbers: 82.70.KjThe AOT(surfactant)-water-decane(oil) three-component microemulsion (AOT denotes sodium di-2-ethylhexylsulfosuccinate) is an ideal system for studying electrical-conductivity percolation phenomena since throughout the isotropic one-phase region it forms a water-in-oil microemulsion. A water-in-oil microemulsion can be effectively considered as a heterogeneous two-component system made up of conducting spherical droplets of water, coated by a monolayer of surfactant molecules, immersed in a continuous nonconducting oil medium. From a liquid-state-physics point of view a water-in-oil microemulsion, can be considered as a collection of conducting hard spheres interacting among themselves via an attractive potential. There has been a number of experimental'"^ and theoretical^''^ studies of electrical-permittivity and -conductivity percolation phenomena in the literature in this AOT-based model microemulsion system over the last few years. In particular, we have recently experimentally established the validity of dynamic scaling for the dielectric relaxation phenomena.^ As far as the static conductivity percolation is concerned, the picture that emerges from the experiments is as follows: The low-frequency conductivity a (below 100 kHz) has a power-law behavior with exponents which are different below and above the percolation threshold. At a given volume fraction of the microemulsion droplets 0, a temperature threshold Tp exists above which there is a dramatic increase in the conductivity. On the other hand, at a given temperature, there exists a volume-fraction threshold 0^ above which the system has high conductivity. Kim and Huang^ showed that 0p and Tp are uniquely related to each other. The locus of percolation points in the r-0 plane, which we shall simply call the percolation line, seems to originate from the vicinity of the cloud-point curve (the critical temperature is about 40 °C and the critical volume fraction about 0.

We study static electrical conductivity of water-in-oil microemulsions in the single-phase region. Below the percolation threshold, the data can be interpreted in terms of a Auctuating-charge model.Above the percolation threshold, in the lamellar region, the conductivity is consistent with randomly oriented~ater layers separated by surfactant sheets. The loci of the percolation thresholds are measured for diA'erent values of water to surfactant molar ratio and explained in terms of a continuum percolation model.