A theory of monolayer phase transitions

We present the exact calculation of the equation of state for a simple model describing the phase transitions occurring in lipid monolayers. The model is of the van der Waals type, but with the density dependent attraction replaced by a long range interaction of another kind. For the size of the molecular hard cores we choose a function which increases with the internal energy of the p possible states of the molecule. As a result of this choice we find p - 1 first order phase transitions between the liquid and the solid state of the monolayer.