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

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Abstract
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 Å 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.