Thermodynamic mechanism of the density anomaly of liquid water

Makoto Yasutomi

doi:10.3389/fphy.2015.00008

Abstract

Although density anomaly of liquid water has long been studied by many different authors up to now, it is not still cleared what thermodynamic mechanism induces the anomaly. The thermodynamic properties of substances are determined by interparticle interactions. We analyze what characteristics of pair potential cause the density anomaly on the basis of statistical mechanics and thermodynamics using a thermodynamically self-consistent Ornstein-Zernike approximation (SCOZA). We consider a fluid of spherical particles with a pair potential given by a hard-core repulsion plus a soft-repulsion and an attraction. We show that the density anomaly occurs when the value of the soft-repulsive potential at hard-core contact is in some proper range, and the range depends on the attraction. Further, we show that the behavior of the excess internal energy plays an essential role in the density anomaly and the behavior is mainly determined by the values of the soft-repulsive potential, especially near the hard core contact. Our results show that most of ideas put forward up to now are not the direct causes of the density anomaly of liquid water.

Highlights

Most liquids become monotonically denser when cooled from room temperature, but liquid water reaches its maximum density at approximately 4◦C, below which it expands to become less dense as it is cooled further
Numerous similar descriptions of pair interactions will be discovered in the coming years, and these will help us to understand why solid water has polymorphic structures and why liquid water has a large number of anomalies
We present a new phase diagram that elucidates the anomalous behavior of liquid water: unusual negative thermal expansion is observed when the value of the potential tail at the hard-core contact is in some proper range that depends on the shape of the attraction; otherwise negative thermal expansion is never observed

Summary

INTRODUCTION

Most liquids become monotonically denser when cooled from room temperature, but liquid water reaches its maximum density at approximately 4◦C, below which it expands to become less dense as it is cooled further. The simplified potential models presented so far have not been shown to reproduce quantitatively the experimental behaviors of liquid water sufficiently well We think that this prevents one from obtaining a conclusive explanation of the density anomaly because the thermodynamic properties of liquids depend strongly on the interparticle interactions. 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].

MODELS

THERMODYNAMIC MECHANISM UNDERLYING THE DENSITY ANOMALY

Findings

CONCLUSIONS AND DISCUSSION