Effect of charge density fluctuations within a droplet on dielectric polarization of ionic microemulsions

A statistical model of the dielectric polarization of ionic water-in-oil microemulsions is proposed. The model makes it possible to describe the effect of temperature and dispersed phase content on the static dielectric permittivity behavior of the microemulsions at a region far below percolation. With the help of this model, the microemulsions formed with the surfactant, sodium bis(2-ethylhexyl) sulfosuccinate (AOT), have been analyzed. The studied systems are considered to consist of nanometer-sized spherical non-interacting water droplets of equal size with negatively charged head groups , staying at the interface and positive counterions Na⁺, distributed in the electrical diffuse double layer of the droplet interior. It can be conjectured that two different mechanisms, that provide an increase of the static dielectric permittivity as a function of temperature, may take place. These may be attributed either to the aggregation of droplets or the temperature growth of polarizability of non-interacting and therefore non-aggregating droplets dispersed in oil. The results support the hypothesis that the experimental temperature behavior of dielectric polarization far below the percolation region is only due to the polarization of a single droplet and not to an aggregation. The droplet polarizability is proportional to the fluctuation mean-square dipole moment of a droplet. It is shown that this mean-square dipole moment and the corresponding value of the dielectric increment, depend upon the equilibrium distribution of counterions within a diffuse double layer. The density distribution of ions is determined by the degree of the dissociation of the ionic surfactant. The dissociation of the ionic surfactant in the system has been analyzed numerically. The relationship between the constant of dissociation and the experimental dielectric permittivity has been ascertained.