The Widom line of supercooled water

Abstract

Water can be supercooled to temperatures as low as−92 °C, the experimental crystal homogeneous nucleation temperatureTH at 2 kbar. Within the supercooled liquid phase its response functions show an anomalousincrease consistent with the presence of a liquid–liquid critical point located in a regioninaccessible to experiments on bulk water. Recent experiments on the dynamics ofconfined water show that a possible way to understand the properties of wateris to investigate the supercooled phase diagram in the vicinity of the Widomline (locus of maximum correlation length) that emanates from the hypothesizedliquid–liquid critical point. Here we explore the Widom line for a Hamiltonianmodel of water using an analytic approach, and discuss the plausibility of thehypothesized liquid–liquid critical point, as well as its possible consequences, on the basisof the assumptions of the model. The present analysis allows us (i) to find ananalytic expression for the spinodal line of the high-density liquid phase, withrespect to the low-density liquid phase, showing that this line becomes flat in theP–T phase diagram in the physical limit of a large number of available orientationsfor 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 forthe hypothesized liquid–liquid critical point coordinates that compare very wellwith Monte Carlo results; and (iii) to show how the Widom line can be locatedby studying the derivative of the probability of forming hydrogen bonds withlocal tetrahedral orientation which can be calculated analytically within thisapproach.