An analytical approach to the anomalous density of water

Abstract

Water, which is essential for the existence of life, has almost a hundred properties that distinguish it from other liquids.In this paper, we will focus on its density, which, unlike the absolute majority of other liquids, increases with increasingtemperature in the vicinity of the solid-liquid transition, for a wide range of pressures, including ambient pressure. Ourapproach will present an analytical thermodynamic formulation for this problem that has as a novelty the introductionof a variable exclusion volume. We will consider the excluded volume a thermodynamic variable that depends onthe system's thermal conditions. This approach will be applied to the two-liquid theory of water, which claims thatwater molecules can be assembled into two different kinds of clusters. At a given state, the relative numbers of theseaggregates can be very sensitive to thermal variations, and, as the excluded volume for each of them is different, whentheir relative number changes, the total excluded volume also changes. We will show how to gather the ideas of a nonconstant excluded volume with the two-liquid theory of water into a new, elegant and non-trivial analytical expression for the density of water. In the end, we compare our expression with experimental data and show that it provides an exact understanding of the anomalous behavior of water density.

Liquid Water: A Single Approach to Its Two Continuous Phase Transitions

“…In the above development, we have determined that the two known water critical points can be predicted by a simple thermodynamic theory that combines the water two-liquid model with the variable excluded volume ( v e ) approach introduced by us . This combination leads to an EoS that generalizes the VdW equation in various ways: it generalizes the excluded volume idea, admitting that the excluded volumes need not be constant, and introduces the excluded pressure, which has a fixed form in the VdW approach but is here computed through the variation of the internal energy with respect to v e , eq .…”

“…The above figure of speech has been used freely in the literature because there is confidence that the two-liquid model (TLM) can explain the phenomena that uniquely characterize water, and some models have been devised to make it. − For example, in a recent paper some of us used this model to show analytically how the TLM can be articulated to quantify the anomalous water density behavior . Here, we will go further by showing how the TLM can describe in a unified way the two known water critical points.…”

Combined Description of the Equation of State and Diffusion Coefficient of Liquid Water Using a Two-State Sanchez–Lacombe Approach

“…The most interesting property (or anomaly) of liquid water is that its density (at atmospheric pressure) exhibits a strongly non-monotonic temperature dependence (with a maximum at T ≈ 277 K), often understood in terms of competition between two or more competing local environments with different density and symmetry whose relative concentration is indeed determined by thermodynamic conditions [ 11 , 12 , 14 , 26 ]. Among many other water anomalies [ 1 , 27 ], we would like to recall that at atmospheric pressure, (1) the isobaric specific heat has a minimum at about T ≈ 308 K, (2) the isothermal compressibility has a minimum at about T ≈ 319 K, and (3) the coefficient of thermal expansion is negative below T ≈ 277 K. These anomalies can be understood, at least qualitatively, on the basis of two coexisting local structures of water and the associated idea of a liquid-liquid critical point (LLCP) [ 2 , 17 , 28 , 29 , 30 ].…”