A thermodynamically hypothesis for explaining the anomalous behavior of water in the supercooled and in the stable liquid region was developed in 1992 by Poole et al [1]. The authors suggested that the sharp increase of response functions are mainly associated with the coexistence of two liquid aqueous phases namely low-density liquid (LDL) and high-density liquid (HDL). The liquid-liquid phase transition (LLPT) between these two states would end on a liquid-liquid critical point (LLCP). An hypothesis that is consistent with a view that considers water as a “mixture” of two distinct structures, being one of the most promissing scenarios for clarifying the anomalous properties of water.

Based on this concept, several of the so-called “two structure equation of state (TSEOS)” were proposed in order to investigate the possibility of a LLCP and the thermodynamic anomalies in supercooled water. One of the most reliable models is the equation of state proposed by Holten and Anisimov [2] which is able to describe most of the available experimental data for supercooled water with just fewer adjustable parameters.

The success of the two structure phenomenological approach lead us to ask for the statistical mechanical origin of this kind of equation, thus providing a connection between microscopic system details and the macroscopic behavior usually called as “anomalous” in the context of liquid water.

In order to discuss waterlike behavior near the liquid-liquid critical temperature, we propose a simple analogy between a fluid and a ferromagnet based on the two states description of spin−1/2 systems using the classical Bragg-Williams mean-field approximation. This framework is used to understand the liquid-liquid phase transition and its relation with waterlike density anomalies and, particularly, the density increase with temperature between 0ºC and 4ºC . Moreover, we also investigate the behavior of thermodynamic response functions, mainly the coefficient of thermal expansion and isothermal compressibility.

[1] Peter H. Poole, Francesco Sciortino, Ulrich Essmann, and H. Eugene Stanley. Phase behaviour of metastable water. Nature, 360(6402):324–328, 11 1992.

[2] V. Holten and M. A. Anisimov. Entropy-driven liquid liquid separation in supercooled water. Scientific Reports, 2(1):713, 12 2012.