Fluctuation mechanism of the dielectric polarization of water-in-oil microemulsions with ionic surfactant

A statistical model is proposed to describe the dielectric polarization of ionic microemulsions at a region far below percolation in which the microemulsions consist of spherical single droplets with water in the central core surrounded by a layer of surfactant molecules. The model describes the effect of temperature and dispersed phase content on the behavior of the dielectric polarization of ionic water-in-oil microemulsions and explains the experimentally observed increase of the static dielectric permittivity as a function of temperature. The microemulsions formed with surfactant sodium bis(2-ethylhexyl) sulfosuccinate have been analyzed with the help of this model. The systems are considered to consist of nanometer-sized spherical noninteracting water droplets of equal size with negatively charged head groups, staying at the interface, and positive counterions, distributed in the electrical diffuse double layer of the droplet interior. It is shown that the droplet polarizability is proportional to the mean-square fluctuation dipole moment of the droplet. This mean-square dipole moment and the corresponding value of the dielectric increment depend on 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 relationship between the dielectric permittivity, the constant of dissociation of surfactant, the content of the dispersed phase, and the temperature has been ascertained.