Tiling in the Geometric Model for Water

Hydrogen bonded liquids like water present a rich thermodynamic behaviour due to the strength and directionality of the bonds. In a recent paper a geometric model based on Bernal’s model for liquids was proposed to study the effects of the hydrogen bonds on the phase transitions of water, under pressure and temperature variations. Water molecules were assumed to stay at the vertices of coordination r (r = 4, 5, 6) of perfectly tiled polygons, and to have four links which allow up to four hydrogen bonds per particle. Mean field calculations yielded a phase diagram with three phases of different densities and a critical point at the end of the coexistence line between the high and low density phases. The three phases were considered to be liquids of different densities. In the present work we have shown that applying some geometric constraints to particle arrangements (thus correcting the system entropy, which was overestimated in the previous work), and allowing a variable number of links per molecule, leads to substantial alteration of the phase diagram. Three phases of different densities are still present, but no critical point appears. Two of the phases are solid, and one phase is amorphous.