Generalized van der Waals theory of liquid-liquid phase transitions

In the framework of the thermodynamic perturbation theory for fluids we study how the phase diagram of an isotropic repulsive soft-core attractive potential, where a liquid-liquid phase transition exists in addition to the standard gas-liquid phase transition, changes by varying the parameters of the potential. We show that there are some regions in a potential parameter space where a high-density liquid-liquid critical point can exist in addition to the conventional gas-liquid critical point. It is also found that there is a correlation between the behavior of the phase diagram as a function of width of the repulsive step and the structure of the correlation function of a reference liquid.