Thermodynamic mechanism of the density anomaly of liquid water

*Correspondence: Makoto Yasutomi, Department of Physics and Earth Sciences, Faculty of Science, University of the Ryukyus, Nishihara-Cho 903-0213, Japan e-mail: [email protected] Although the density anomaly of liquid water has long been studied by many different authors, it is still not clear what thermodynamic mechanism induces the anomaly. The thermodynamic properties of substances are determined by interparticle interactions. We analyze what characteristics of the pair potential cause the density anomaly on the basis of statistical mechanics and thermodynamics using a thermodynamically self-consistent Ornstein-Zernike approximation. 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 that the range depends on the attraction. Furthermore, we show 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 hard-core contact. Our results show that most of the ideas put forward up to now do not explain the direct causes of the density anomaly of liquid water. It has been known for a long time that these ideas tell us nothing about what causes the negative thermal expansion at temperatures below 4 C. ◦