Structure of self-assembly amphiphilic systems: Relation between phenomenological parameters and microscopic potential parameters

We study the correlation and structural functions of symmetric amphiphilic systems. The systems are modelled by a double Kac potential and their structure is analyzed analytically in the random phase approximation (RPA) of the liquid state theory combined with the hard-sphere (HS) reference system. The microscopic approximation applied to the model yields a theory consistent with the phenomenological Landau-Ginzburg theory of microemulsions. When the amount of surfactant in the microemulsion is increasing, the behaviour of the total correlation function changes from an exponential decreasing to a damped oscillatory decaying, and the peak emerging in the structure factor of amphiphilic systems grows up in agreement with the small-angle neutron scattering experiments. The Lifshitz line at which the peak in the structure factor is no longer at the zero wave vector - could be reached with specific values for the parameters characterizing the structure of the model.