| Water is up to now the most important liquid for the presence of life on the earth. At the same time, is does not behave like most liquids: for example, starting from normal conditions (pressure ∼1 bar, temperature ∼25 C), it becomes less viscous upon compression and less dense upon cooling.; The molecular potentials used to simulate water have complex functional form depending both on the relative distance and the relative orientation of the molecules; such potentials are unfeasible of simple analytical treatment. We find that a simple spherical symmetrical potential with a concave region in the repulsive part can reproduce qualitatively all the known anomalies of liquid water. In particular, we solve the model analytically in one dimension and via molecular dynamics simulation in two dimensions; a mean field-like analysis of the model in two dimensions provides indications for the existence of a liquid-liquid critical point in the super-cooled region of the phase diagram.; We then perform three dimensional simulations of a realistic model of water in order to analyze the relation between the anomalies in the statics (expansion upon cooling) and in the dynamics (increase of the diffusivity upon compression). With the use of the concepts of the recently introduced landscape theory, we find that the diffusivity D is a monotonic increasing function of the configurational entropy Sconf (i.e. the number of local potential energy minima sampled by the system). Extrapolating the results of the simulations to lower temperature, we find that the presence of a liquid-liquid transition at temperatures and pressures at which the system is predicted to be frozen in a non-diffusive D = 0 state. |
