Four scenarios have been proposed for the low--temperature phase behavior of liquid water, each predicting different thermodynamics. The physical mechanism which leads to each is debated. Moreover, it is still unclear which of the scenarios best desc
ribes water, as there is no definitive experimental test. Here we address both open issues within the framework of a microscopic cell model by performing a study combining mean field calculations and Monte Carlo simulations. We show that a common physical mechanism underlies each of the four scenarios, and that two key physical quantities determine which of the four scenarios describes water: (i) the strength of the directional component of the hydrogen bond and (ii) the strength of the cooperative component of the hydrogen bond. The four scenarios may be mapped in the space of these two quantities. We argue that our conclusions are model-independent. Using estimates from experimental data for H bond properties the model predicts that the low-temperature phase diagram of water exhibits a liquid--liquid critical point at positive pressure.
By the Wolffs cluster Monte Carlo simulations and numerical minimization within a mean field approach, we study the low temperature phase diagram of water, adopting a cell model that reproduces the known properties of water in its fluid phases. Both
methods allows us to study the water thermodynamic behavior at temperatures where other numerical approaches --both Monte Carlo and molecular dynamics-- are seriously hampered by the large increase of the correlation times. The cluster algorithm also allows us to emphasize that the liquid--liquid phase transition corresponds to the percolation transition of tetrahedrally ordered water molecules.
Experiments in bulk water confirm the existence of two local arrangements of water molecules with different densities, but, because of inevitable freezing at low temperature $T$, can not ascertain whether the two arrangements separate in two phases.
To avoid the freezing, new experiments measure the dynamics of water at low $T$ on the surface of proteins, finding a crossover from a non-Arrhenius regime at high $T$ to a regime that is approximately Arrhenius at low $T$. Motivated by these experiments, Kumar et al. [Phys. Rev. Lett. 100, 105701 (2008)] investigated, by Monte Carlo simulations and mean field calculations, the relation of the dynamic crossover with the coexistence of two liquid phases in a cell model for water and predict that: (i) the dynamic crossover is isochronic, i.e. the value of the crossover time $tau_{rm L}$ is approximately independent of pressure $P$; (ii) the Arrhenius activation energy $E_{rm A}(P)$ of the low-$T$ regime decreases upon increasing $P$; (iii) the temperature $T^*(P)$ at which $tau$ reaches a fixed macroscopic time $tau^*geq tau_{rm L}$ decreases upon increasing $P$; in particular, this is true also for the crossover temperature $T_{rm L}(P)$ at which $tau=tau_{rm L}$. Here, we compare these predictions with recent quasi elastic neutron scattering (QENS) experiments performed by X.-Q. Chu {it et al.} on hydrated proteins at different values of $P$. We find that the experiments are consistent with these three predictions.
