Scaled Equation of State for Supercooled Water near the Liquid-Liquid Critical Point

We have developed a scaled parametric equation of state to describe and predict thermodynamic properties of supercooled water. The equation of state, built on the growing evidence that the critical point of supercooled liquid-liquid water separation exists, is universal in terms of theoretical scaling fields and is shown to belong to the Ising-model class of universality. The theoretical scaling fields are postulated to be analytical combinations of the physical fields, pressure, and temperature. The equation of state enables us to accurately locate the “Widom line” (the locus of stability minima) and determine that the critical pressure is considerably lower than predicted by computer simulations.

Figure 1

(a) Phase diagram for water with vapor-liquid and liquid-liquid critical points. Solid curves are vapor-liquid, liquid-liquid, and liquid-solid phase transitions; dashed is the Widom line; dotted is the compressibility maxima; crosses are literature estimates for the liquid-liquid critical point. $C$ is the vapor-liquid critical point; $C^{\prime }$ is the liquid-liquid critical point predicted by our equation of state. (b) The vicinity of the liquid-liquid critical point [5, 8].

Figure 2

Heat-capacity measurements (★) [15] compared with the heat capacity predicted by our scaling parametric equation of state (solid curve) for a critical point of $P_c=27\mathrm{MPa}$, $T_c=232\mathrm{K}$. Noncritical background plotted as a thin solid curve.

Figure 3

Isothermal compressibility experimental data [19] at 10 MPa (○), 50 MPa (▵), 100 MPa (◇), 150 MPa (★), and 190 MPa (□), compared with our prediction at the same pressures (solid curves).

Figure 4

Thermal expansivity experimental data [20] (▴), at ambient pressure, compared with our prediction (solid curve). Noncritical background plotted as a thin solid curve.