The metastable T−P phase diagram and anomalous thermodynamic properties of supercooled water

Abstract

The metastable T−P phase diagram and the anomalies of the thermodynamic properties of supercooled water are calculated on the basis of a two-level thermodynamic model. Water is considered as a mixture of two components which differ in atomic configurations and correspond to low-density amorphous (lda) and high-density amorphous (hda) ice. The expression for the Gibbs potential of water is written in the form which is analogous to that of usual regular binary solutions. But this model considers the concentration, c, of the components, as a pressure and temperature-dependent internal parameter. There are only four constants in the expression for the Gibbs potential: the differences in the specific volumes, entropies, and energies of the two components and the mixing energy of the components whose values are ΔV0=−3.8 cm3/mol, ΔS0=4.225 J/mol, ΔE0=1037 J/mol, and U=3824 J/mol, respectively. The lda−hda phase equilibrium line terminates at the critical point, Tcr=230 K and Pcr=0.173 kbar, the second critical point in the phase diagram of water. The anomalous thermal dependence of the specific volume, the heat expansion coefficient, and the specific heat of water calculated for the atmospheric pressure is in a good quantitative agreement with the available experimental data. Thus anomalous properties of supercooled water are well explained by the occurrence of the second critical point close to the atmospheric pressure. The absolute value of parameter c is not crucial for the thermal behavior of properties, instead, the anomalies in water are due to the dependence on pressure and temperature. The parameter c behavior is analyzed in various pressure and temperature ranges around the second critical point. The thermal dependence of parameter c is very weak in the temperature range of 290–350 K at atmospheric pressure. As a consequence, the thermodynamic properties of water behave in this range like those of a normal liquid though water stays a mixture of two components, lda-like and hda-like, in an approximate proportion 2:3.