Liquid Polymorphism and Double Criticality in a Lattice Gas Model

We analyze the possible phase diagrams of a simple model for an associating liquid proposed previously. Our two-dimensional lattice model combines oreintati onal ice-like interactions and \"{}Van der Waals\"{} interactions which may be repulsive, and in this case represent a penalty for distortion of hydrogen bonds in the presence of extra molecules. These interactions can be interpreted in terms of two competing distances, but not necessarily soft-core. We present mean -field calculations and an exhaustive simulation study for different parameters which represent relative strength of the bonding interaction to the energy penalty for its distortion. As this ratio decreases, a smooth disappearance of the doubl e criticality occurs. Possible connections to liquid-liquid transitions of molecul ar liquids are suggested