Liquid water has anomalous liquid properties, such as its density maximum at 4 °C. An attempt at theoretical explanation proposes a liquid-liquid phase transition line in the supercooled liquid state, with coexisting low-density liquid (LDL) and high-density liquid (HDL) states. This line terminates at a critical point. It is assumed that the LDL state possesses mesoscopic tetrahedral structures that give it solidlike properties, while the HDL is a regular random liquid. But the short-lived nature of these solidlike structures makes them difficult to detect directly. We take a thermodynamic approach instead and calculate the thermodynamic Ricci curvature scalar R in the metastable liquid regime. It is believed that solidlike structures signal their presence thermodynamically by a positive sign for R, with a negative sign typically present in less organized fluid states. Using thermodynamic data from ST2 computer simulations fit to a mean field (MF) two state equation of state, we find significant regimes of positive R in the LDL state, supporting the proposal of solidlike structures in liquid water. In addition, we review the theory, compute critical exponents, demonstrate the large reach of the MF critical regime, and calculate the Widom line using R.
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The Widom line was defined as the “locus of maximum correlation length” by Franzese and Stanley,69 a definition much seen in the literature. Earlier, however, Griffiths and Wheeler70 referred to the concept of the Widom line as the “linear extension of the coexistence curve in the p − T plane.” This concept may be challenged since the behavior at the critical point is nonanalytic beyond MF theory. Widom and Rowlinson71 focussed on the critical isochor and refer to “either the critical isochor or the locus on which above TC.” Holten et al.,54 in their MF context, take the Widom line to be the analytic continuation of the phase transition line, and this is the picture that we feature here.
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