Perturbation theory for water with an associating reference fluid

The theoretical description of the thermodynamics of water is challenged by the structural transition towards tetrahedral symmetry at ambient conditions. As perturbation theories typically assume a spherically symmetric reference fluid, they are incapable of accurately describing the liquid properties of water at ambient conditions. In this paper we address this problem by introducing the concept of an associated reference perturbation theory (APT). In APT we treat the reference fluid as an associating hard sphere fluid which transitions to tetrahedral symmetry in the fully hydrogen bonded limit. We calculate this transition in a theoretically self-consistent manner without appealing to molecular simulations. This associated reference provides the reference fluid for a second order Barker-Henderson perturbative treatment of the long-range attractions. We demonstrate that this approach gives a significantly improved description of water as compared to standard perturbation theories.

Figure 1

Diagram of interacting conical square-well association sites.

Figure 2

Comparison of APT vapor pressure model results (curve) to experimental data [33].

Figure 3

(a) T-ρ phase diagram for water. Curve gives APT model results and symbols give experiment [33]. (b) Zoomed in on saturated liquid densities near ambient conditions. Solid curve gives APT results and dashed curve gives HSPT results.

Figure 4

(a) Reference system coordination number for a saturated liquid in a shell of 3.3 Å. Solid curve gives APT and dashed curve gives HSPT. Symbols give molecular simulation results [34, 35] using iAMOEBA [4] (circles) and TIP4P/2005 [3] (crosses). (b) Fraction of water molecules bonded four times for a saturated liquid predicted from APT.

Figure 5

Volume expansivity of water versus $T$ at atmospheric pressure. Curves have same meaning as Fig. 4 and symbols give experimental data [36].

Figure 6

(a) Isothermal compressibility versus $T$ at a pressure of 1 bar. Lines have same meaning as Fig. 4 and symbols give data [37]. (b) Isobaric heat capacity at 1 bar. Symbols give experimental data [38].