Interparticle interactions between water molecules

Abstract

We determined many functional representations of interparticle interactions between water molecules, all of which reproduce the experimentally measured density-temperature relation at 1 bar with an accuracy better than obtained by previous models. Numerous similar descriptions of pair interactions will be discovered increasingly in the coming years, which will help us to understand why solid water has polymorphic structures and why liquid water has a large number of anomalies. We used a self-consistent Ornstein-Zernike approximation (SCOZA) with a potential given by multi-Yukawa terms. Because any smooth potential function can be fitted by multi-Yukawa terms, the method can be applied to various types of fluids. We also present a new simple fitting technique that makes the application of the SCOZA to any type of liquid much easier compared to a conventional Yukawa fit. Our new SCOZA fitting technique is among the most useful methods for determining the pair interaction between molecules of any liquid, and the potential will be helpful in improving realistic models.

Thermodynamic mechanism of the density anomaly of liquid water

“…It is also found that the behavior of excess internal energy plays an essential role in the density anomaly and that the behavior is mainly determined by the value of the soft-repulsive potential, especially near the hardcore contact, depending on the attraction. Our results show that most of the ideas put forward up to now, such as the second critical point hypothesis, simple two-state model, liquid-liquid phase transition model, clathrate model, network model, hydrogen bonding, orientation-dependent potential, and so on, do not explain the direct causes of the density anomaly of liquid water, as we discussed in our previous article [41].…”

“…As a result, the liquid expands to become less dense as it is cooled further in the range of kT < kT 4 at a specified pressure. The behavior of the isothermal pressure-density curves shown in Figures 2, 3 is just what one can infer from the shape of the experimentally measured isobaric density-temperature curve of liquid water, which is exhibited in Figure 2 in Yasutomi [41] by open circles.…”

“…Figure 1 shows these potentials except for φ 6 (r). The tail φ 6 (r) is the same as φ 5 (r) in Yasutomi [41]. The diameter of the hard-core σ u is used as the unit of length and the depth of the potential ε u as the unit of energy.…”

“…We express the physical quantities by the same symbols used in Yasutomi [41], and the numerical computations are performed by using the same method described in Pini et al [35,41]. Tables 3, 4 show the density grid ρ, the temperature grid β, the density ρ 0 at which we made use of the so-called high-temperature approximation [43], and β f ; numerical computations are performed in the range of 0 < β < β f .…”

“…Such a force (hereafter for simplicity referred to as the "anomaly force") is the immediate cause of the density anomaly of liquid water [41]. Our study is blind to freezing and, more generally, to the solid phases of the model system (see e.g., [42]), but it gives significant insight into the thermodynamic properties of water in these phases.…”