Water is the most abundant liquid on earth and also the substance with the largest number of anomalies in its properties. It is a prerequisite for life and as such a most important subject of current research in chemical physics and physical chemistry. In spite of its simplicity as a liquid, it has an enormously rich phase diagram where different types of ices, amorphous phases, and anomalies disclose a path that points to unique thermodynamics of its supercooled liquid state that still hides many unraveled secrets. In this review we describe the behavior of water in the regime from ambient conditions to the deeply supercooled region. The review describes simulations and experiments on this anomalous liquid. Several scenarios have been proposed to explain the anomalous properties that become strongly enhanced in the supercooled region. Among those, the second critical-point scenario has been investigated extensively, and at present most experimental evidence point to this scenario. Starting from very low temperatures, a coexistence line between a high-density amorphous phase and a low-density amorphous phase would continue in a coexistence line between a high-density and a low-density liquid phase terminating in a liquid–liquid critical point, LLCP. On approaching this LLCP from the one-phase region, a crossover in thermodynamics and dynamics can be found. This is discussed based on a picture of a temperature-dependent balance between a high-density liquid and a low-density liquid favored by, respectively, entropy and enthalpy, leading to a consistent picture of the thermodynamics of bulk water. Ice nucleation is also discussed, since this is what severely impedes experimental investigation of the vicinity of the proposed LLCP. Experimental investigation of stretched water, i.e., water at negative pressure, gives access to a different regime of the complex water diagram. Different ways to inhibit crystallization through confinement and aqueous solutions are discussed through results from experiments and simulations using the most sophisticated and advanced techniques. These findings represent tiles of a global picture that still needs to be completed. Some of the possible experimental lines of research that are essential to complete this picture are explored.

The excess entropy, S e , defined as the difference between the entropies of the liquid and the ideal gas under identical density and temperature conditions, is shown to be the critical quantity connecting the structural, diffusional and density anomalies in water-like liquids. Based on simulations of silica and the two-scale ramp liquids, water-like density and diffusional anomalies can be seen as consequences of a characteristic non-monotonic density dependence of S e . The relationship between excess entropy, the order metrics and the structural anomaly can be understood using a pair correlation approximation to S e . 61.20.Qg,05.20.Jj The behaviour of water is anomalous when compared to simple liquids for which the structure and dynamics is dominated by strong, essentially isotropic, short-range repulsions [1,2].For example, over certain ranges of temperature and pressure,the density of water increases with temperature under isobaric conditions (density anomaly) while the self-diffusivity increases with density under isothermal conditions (diffusional anomaly). Experiments as well as simulations suggest that the anomalous thermodynamic and kinetic properties of water are due to the fluctuating, three-dimensional, locally tetrahedral hydrogen-bonded network. Water-like anomalies are seen in other tetrahedral network-forming liquids, such as silica, as well as in model liquids with isotropic core-softened or two-scale pair potentials [3,4,5,6,7,8,9,10,11].In the case of liquids such as water and silica, a quantitative connection between the structure of the tetrahedral network and the macroscopic density or temperature variables can be made by introducing order metrics to gauge the type as well as the extent of structural order [6,7]. The local tetrahedral order parameter, q tet , associated with an atom i (e.g. Si atom in SiO 2 ) is defined aswhere ψ jk is the angle between the bond vectors r ij and r ik where j and k label the four nearest neighbour atoms of the same type [6]. The translational order parameter, τ , measures the extent of pair correlations present in the system and is defined aswhere ξ = rρ 1/3 , r is the pair separation and ξ c is a suitably chosen cut-off distance [12].Since τ increases as the random close-packing limit is approached, it can be regarded as measuring the degree of density ordering. At a given temperature, q tet will show a maximum and τ will show a minimum as a function of density; the loci of these extrema in the order define a structurally anomalous region in the density-temperature (ρT ) plane. Within this structurally anomalous region, the tetrahedral and translational order parameters are found to be strongly correlated. The region of the density anomaly, where (∂ρ/∂T ) P > 0, is bounded by the structurally anomalous region. The diffusionally anomalous region ((∂D/∂ρ) T > 0) closely follows the boundaries of the structurally anomalous region, specially at low temperatures. In water, the structurally anomalous region encloses the region of anomalous diffusivit...

Excess-entropy scaling relationships for diffusivity and viscosity of Lennard-Jones chain fluids are tested using molecular dynamics simulations for chain sizes that are sufficiently small that chain entanglement effects are insignificant. The thermodynamic excess entropy S(e) is estimated using self-associating fluid theory (SAFT). A structural measure of the entropy S(2) is also computed from the monomer-monomer pair correlation function, g(m)(r). The thermodynamic and structural estimators for the excess entropy are shown to be very strongly correlated. The dimensionless center-of-mass diffusivities, D(cm) (*), obtained by dividing the diffusivities by suitable macroscopic reduction parameters, are shown to conform to the excess entropy scaling relationship, D(cm) (*)=A(n) exp(alpha(n)S(e)), where the scaling parameters depend on the chain length n. The exponential parameter alpha(n) varies as -(1n) while A(n) varies approximately as n(-0.5). The scaled viscosities obey a similar relationship with scaling parameters B(n) and beta(n) where beta(n) varies as 1n and B(n) shows an approximate n(0.6) dependence. In accordance with the Stokes-Einstein law, for a given chain length, alpha(n)=-beta(n) within statistical error. The excess entropy scaling parameters associated with the transport properties therefore display a simple dependence on chain length.

Structural, density, entropy, and diffusivity anomalies of the TIP4P/2005 model of water are mapped out over a wide range of densities and temperatures. The locus of temperatures of maximum density (TMD) for this model is very close to the experimental TMD locus for temperatures between 250 and 275 K. Four different water models (mTIP3P, TIP4P, TIP5P, and SPC/E) are compared with the TIP4P/2005 model in terms of their anomalous behavior. For all the water models, the density regimes for anomalous behavior are bounded by a low-density limit at around 0.85-0.90 g cm(-3) and a high-density limit at about 1.10-1.15 g cm(-3). The onset temperatures of the density anomaly in the various models show a much greater variation, ranging from 202 K for mTIP3P to 289 K for TIP5P. The order maps for the various water models are qualitatively very similar with the structurally anomalous regions almost superimposable in the q(tet)-τ plane. Comparison of the phase diagrams of water models with the region of liquid-state anomalies shows that the crystalline phases are much more sensitive to the choice of water models than the liquid state anomalies; for example, SPC/E and TIP4P/2005 show qualitatively similar liquid state anomalies but very different phase diagrams. The anomalies in the liquid in all the models occur at much lower pressures than those at which the melting line changes from negative to positive slope. The results in this study demonstrate several aspects of structure-entropy-diffusivity relationships of water models that can be compared with experiment and used to develop better atomistic and coarse-grained models for water.

Abstract. The thermodynamic liquid-state anomalies and associated structural changes of the Stillinger-Weber family of liquids are mapped out as a function of the degree of tetrahedrality of the interaction potential, focusing in particular on tetrahedrality values suitable for modeling C, H2O, Si, Ge and Sn. We show that the density anomaly, associated with a rise in molar volume on isobaric cooling, emerges at intermediate tetrahedralities (e.g. Ge, Si and H2O) but is absent in the low (e.g. Sn) and high (e.g. C) tetrahedrality liquids. The rise in entropy on isothermal compression associated with the density anomaly is related to the structural changes in the liquid using the pair correlation entropy. An anomalous increase in the heat capacity on isobaric cooling exists at high tetrahedralities but is absent at low tetrahedralities (e.g. Sn). Structurally, this heat capacity anomaly originates in a sharp rise in the fraction of four-coordinated particles and local tetrahedral order in the liquid as its structure approaches that of the tetrahedral crystal.