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 (σ) measured as a function of temperature (T) and the volume fraction (Φ) 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 σ, implying that the main charge carrier is the cation species (Na⁺) dissolved in and transported with water. Given the relation D_exchange = 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 σTΦ^-1 and D_exchange was first confirmed to show asymptotic behavior in which σT^-1 ∼ (D _exchange)^-β [β = 3.2 for -10.7 ≤ log (D _exchange) ≤ -10.0 and β= 1.3 for -10.0 ≤ log (D _exchange) ≤ -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 β 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.