Scaling relation between electrical conductivity percolation and water diffusion coefficient in sodium bis(2-ethylhexyl) sulfosuccinate-based microemulsion

We investigated the conductivity percolation mechanism of a water-in-oil (W/O) microemulsion composed of sodium bis(2-ethylhexyl) sulfosuccinate (AOT), D2O, and decane using impedance spectroscopy and the pulsed-gradient spin-echo (PGSE) NMR technique. The electrical conductivity (sigma) measured as a function of temperature (T) and the volume fraction (Phi) of water droplets show a marked increase near room temperature. The PGSE NMR measurements show that the water diffusion coefficient (D-water) is responsible for sigma, implying that the main charge carrier is the cation species (Na+) dissolved in and transported with water. Given the relation D-exchange equivalent to D-water - D-droplet, where D-exchange and D-droplet are diffusion coefficients for the exchange of water between water droplets and for the whole host droplet, respectively, a quantitative scaling relation between reduced conductivity sigmaTPhi(-1) and D-exchange was first confirmed to show asymptotic behavior in which sigmaTPhi(-1) similar to (D-exchange)(beta) [beta = 3.2 for -10.7 less than or equal to log (D-exchange) less than or equal to -10.0 and beta = 1.3 for -10.0 less than or equal to log (D-exchange) less than or equal to -9.3]. This reveals that a common mechanism governs both conductivity percolation and the water exchange between droplets in AOT-based W/O microemulsion. The discontinuity of the exponent beta at log (D-exchange) ca. 10.0 indicates a change in the mechanism of water exchange between the droplets, resulting mainly from Na cation distribution in a droplet.