Simple physical model of liquid water

We propose a simple two-state model of water to explain the unusual thermodynamic and dynamic behavior of liquid water. Our model is based on a physical picture that there exist two competing orderings in water, namely, density ordering and bond ordering. Short-range bond ordering leads to the formation of a rather stable locally favored structure (in a ground state) in a sea of disordered normal-liquid structures (in an excited state). Its fraction increases with decreasing temperature, obeying a Boltzmann factor. The concept of a “symmetry (or volume) element” is introduced to specify such locally favored structures in an unambiguous manner. The most probable candidate of such locally favored structures is an “octameric unit,” which is an elementary structural unit of ice Ih. According to this picture, the uniqueness of water comes from that below the crossover pressure $P_c$ $\text{(∼2 \hspace{0.17em}}\mathrm{kbar})$ the short-range bond order can develop into the long-range order (crystallization into ice Ih). Note that in ordinary liquids crystallization is induced only by density ordering, while in water it is induced by bond ordering below $P_c,$ while by density ordering above $P_c.$ Our model predicts that the anomalous parts of density $\mathrm{\rho ,}$ isothermal compressibility $K_T,$ heat capacity at constant pressure $C_P,$ and the activation energy of viscosity $\eta$ should all be proportional to the Boltzmann factor in the temperature region, where “bulk water” is in a liquid state. It is found that this prediction well explains not only the thermodynamic anomaly of $\mathrm{\rho ,}$ $K_T,$ and $C_P,$ but also the dynamic anomaly of $\mathrm{\eta ,}$ including their pressure dependencies. This demonstrates that the anomaly of “bulk water” is a direct consequence of short-range bond ordering and it is not due to the thermodynamic singularity, at least above −20 to −30° C. Our model indicates a new possibility that the viscosity anomaly of water may also be explained by the same mechanism as that of the thermodynamic anomaly; namely, neither critical anomaly nor slow dynamics associated with a glass transition may be a major cause of the dynamic anomaly of water above −20 $°\mathrm{C}$ . We also point out that the water’s thermodynamic and dynamic anomaly is not necessarily related to the low-temperature phase behavior of liquid water in an obvious manner, contrary to the common belief.