Liquid-liquid critical point in a simple analytical model of water

A statistical model for a simple three-dimensional Mercedes-Benz model of water was used to study phase diagrams. This model on a simple level describes the thermal and volumetric properties of waterlike molecules. A molecule is presented as a soft sphere with four directions in which hydrogen bonds can be formed. Two neighboring waters can interact through a van der Waals interaction or an orientation-dependent hydrogen-bonding interaction. For pure water, we explored properties such as molar volume, density, heat capacity, thermal expansion coefficient, and isothermal compressibility and found that the volumetric and thermal properties follow the same trends with temperature as in real water and are in good general agreement with Monte Carlo simulations. The model exhibits also two critical points for liquid-gas transition and transition between low-density and high-density fluid. Coexistence curves and a Widom line for the maximum and minimum in thermal expansion coefficient divides the phase space of the model into three parts: in one part we have gas region, in the second a high-density liquid, and the third region contains low-density liquid.

Figure 1

One layer of the hexagon of the icelike lattice structure and a pair interaction used for bookkeeping to avoid triple counting.

Figure 2

The three states of the model: (1) hydrogen bonded, (2) van der Waals, and (3) nonbonded.

Figure 3

Temperature dependence of the molar volume, thermal expansion coefficient, isothermal compressibility, and heat capacity for pressures $p^{*}=0.19$ (green) and $p^{*}=0.12$ (red) and comparison of analytical theory (lines) with results of computer simulations (symbols) [29, 30].

Figure 4

Temperature dependence of the density for various pressures (red solid line), high-density liquid–low-density liquid coexistence line (green long-dashed line), liquid-gas density coexistence line (pink dotted line), and maximum densities (green dashed line).

Figure 5

Low-density fraction $f_s$ and high-density fraction $f_{HB}$ as a function of temperature for various isotherms ($p^{*}=0.06$–0.23).

Figure 6

Phase diagram of the noncrystalline phases of water. Red solid line is liquid-liquid and green dashed line liquid-gas coexistence line.

Figure 7

Coexistence line (red solid line) with position of extremes of heat capacity (green long-dashed line), isothermal compressibility (blue dashed line), and thermal expansion coefficient (pink dotted line) for liquid-liquid (left) and liquid-gas (right) transition and supercritical region.

Figure 8

Phase space of water model is split into three parts: LD- low-density liquidlike phase, HD- high-density liquidlike phase, and G- gaslike phase.