Breakdown of the Stokes–Einstein Equation for Solutions of Water in Oil Reverse Micelles

An experimental study is presented for the reverse micellar system of 15% by mass polydisperse hexaethylene glycol monodecylether (C₁₀E₆) in cyclohexane with varying amounts of added water up to 4% by mass. Measurements of viscosity and self-diffusion coefficients were taken as a function of temperature between 10 and 45 °C at varying sample water loads but fixed C₁₀E₆/cyclohexane composition. The results were used to inspect the validity of the Stokes–Einstein equation for this system. Unreasonably small reverse average micelle radii and aggregation numbers were obtained with the Stokes–Einstein equation, but reasonable values for these quantities were obtained using the ratio of surfactant-to-cyclohexane self-diffusion coefficients. While bulk viscosity increased with increasing water load, a concurrent expected decrease of self-diffusion coefficient was only observed for the surfactant and water but not for cyclohexane, which showed independence of water load. Moreover, a spread of self-diffusion coefficients was observed for the protons associated with the ethylene oxide repeat unit in samples with polydisperse C₁₀E₆ but not in a sample with monodisperse C₁₀E₆. These findings were interpreted by the presence of reverse micelle to reverse micelle hopping motions that with higher water load become increasingly selective toward C₁₀E₆ molecules with short ethylene oxide repeat units, while those with long ethylene oxide repeat units remain trapped within the reverse micelle because of the increased hydrogen bonding interactions with the water inside the growing core of the reverse micelle. Despite the observed breakdown of the Stokes–Einstein equation, the temperature dependence of the viscosities and self-diffusion coefficients was found to follow Arrhenius behavior over the investigated range of temperatures.