Theory and experiment of electrical conductivity and percolation locus in water-in-oil microemulsions

An extensive set of measurements of low-frequency conductivity {σ} of a three-component microemulsion system, sodium-di-2-ethyl-hexylsulfosuccinate (AOT)-water-decane, as a function of temperature (T from 10 to 50 ^∘{}C) and volume fraction of the dispersed phase ({φ} from 0.098 to 0.65) has been made. The measurements were made at a fixed value of the water-to-surfactant molar ratio equal to 40.8, where the microemulsion consists of AOT-coated water droplets, 85 {} in radius, dispersed in oil. {σ} can be quantitatively calculated at low {φ} by means of a charge fluctuation model of Eicke et al., while it can be interpreted for higher vlaues of {φ} in terms of power-law behavior with indices related to the dynamic percolation picture below the threshold and the static one above it. The percolation locus in {φ}-T plane has been determined starting from the vicinity of the lower consolute point up to {φ}=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.