A geometric model for cold water and liquid-liquid transitions

Water is an associated liquid in which the main intermolecular interaction is the hydrogen bond (HB) which is limited to four per atom, independently of the number of neighbours. We have considered a hydrogen bond net superposed on Bernal's geometric model for liquids, which allows for different local environments for the liquid particles. In this study, a mean-field treatment of the two-dimensinal version of the model is discussed. Under pressure the model exhibits three phases of different densities and a coexistence line ending in a critical point between low and high density phases. Entropy of the HB network plays an essential role in defining the slope of the coexistence line. The model behaviour might be of interest in describing supercooled water and liquid-liquid transitions of other substances.