content_image/363056.jpg content_image/363055.jpg content_image/363054.jpg content_image/363057.jpg content_image/363058.jpg
the solvent and with each other, such that we can assume 

With this assumption the Hamiltonian takes the simpler form 

<img src='content_image/363056.jpg'>

<img src='content_image/363055.jpg'>

Note that the SR contribution to the energy depends only on ˆ φ 2 when the assumptions (7) are valid; otherwise the full expression (5) has to be considered. We assume J$_{ss}$ ≫ J$_{ρρ}$ , so that the system can phase separate into two phases, one of them rich in the first- and the other one rich in the second component of the solvent, rather than into a phase rich in the 3-rd component and a phase rich in the 4-th component of the mixture. The coupling J$_{sρ}$ > 0 signals that ions preferentially dissolve in the first component of the solvent. 

When the species 3 and 4 are charged, then Coulomb interactions between them are present in addition to the short range interactions. In the truly microscopic model one should take into account polarizability of the solvent, and the problem becomes very difficult. In the semi-microscopic description the effect of polarizability of the solvent is included only through the dielectric permittivity. The dielectric permittivity depends on the composition and, in the case of spatial inhomogeneities of the composition, the dielectric permittivity is a functional of the solvent densities and depends on x . The electrostatic energy-density e$_{e}$ in this case has the form [9, 15] 

<img src='content_image/363054.jpg'>

where 

<img src='content_image/363057.jpg'>

<img src='content_image/363058.jpg'>

