The Widom line of supercooled water

Water can be supercooled to temperatures as low as -92 degrees C, the experimental crystal homogeneous nucleation temperature T-H at 2 kbar. Within the supercooled liquid phase its response functions show an anomalous increase consistent with the presence of a liquid-liquid critical point located in a region inaccessible to experiments on bulk water. Recent experiments on the dynamics of confined water show that a possible way to understand the properties of water is to investigate the supercooled phase diagram in the vicinity of the Widom line (locus of maximum correlation length) that emanates from the hypothesized liquid - liquid critical point. Here we explore the Widom line for a Hamiltonian model of water using an analytic approach, and discuss the plausibility of the hypothesized liquid-liquid critical point, as well as its possible consequences, on the basis of the assumptions of the model. The present analysis allows us (i) to find an analytic expression for the spinodal line of the high-density liquid phase, with respect to the low-density liquid phase, showing that this line becomes flat in the P-T phase diagram in the physical limit of a large number of available orientations for the hydrogen bonds, as recently seen in simulations and experiments (Xu et al 2005 Proc. Natl Acad. Sci. 102 16558); (ii) to find an estimate of the values for the hypothesized liquid-liquid critical point coordinates that compare very well with Monte Carlo results; and (iii) to show how the Widom line can be located by studying the derivative of the probability of forming hydrogen bonds with local tetrahedral orientation which can be calculated analytically within this approach.