(9g) Metastable Liquid-Liquid Criticality in Supercooled Wail Water

The hypothesis that the anomalous behavior of liquid water is related to the existence of a second critical point in deeply supercooled states has long been the subject of intense debate. Recent, sophisticated experiments designed to observe the transformation between the two subcritical liquids on nano- and microsecond timescales, along with demanding numerical simulations based on classical (rigid) models parametrized to reproduce thermodynamic properties of water, have provided support to this hypothesis. A stronger numerical proof requires demonstrating that the critical point, which occurs at temperatures and pressures far from those at which the models were optimized, is robust with respect to model parameterization, specifically with respect to incorporating additional physical effects. Here we show that a liquid-liquid critical point can be rigorously located also in the WAIL model of water [J. Chem. Phys. 137, 014510 (2012)], a model parameterized using ab-initio calculations only. The model incorporates two features not present in many previously-studied water models: it is both flexible and polarizable, properties which can significantly influence the phase behavior of water. The observation of the critical point in a model in which the water-water interaction is estimated only using quantum ab-initio calculations confirms that the existence of two distinct liquids is a robust feature in the free energy landscape of supercooled water. Intriguingly, the WAIL model contains a critical point at milder temperatures and pressures than several previously-studied models.

Precise identification of this critical point is facilitated by several statistical-mechanical tools. First among these is the weighted-histogram analysis method, which allows observed distributions in thermodynamic properties – in this case, density and energy – to be reweighted to infer those at arbitrary temperatures and pressures. Those reweighted distributions are then compared to those observed in the 3D Ising model at its critical point: because both belong to the same universality class, the critical point can be identified when an appropriate linear combination of energy and density takes the same distribution as that of the magnetization of the critical Ising ferromagnet. This provides an objective function that can be optimized to find the critical temperature and pressure.

The existence of an LLT, and of the two distinct structures associated with it, also has implications for the nucleation of ice from the supercooled liquid. Nucleation from low-density liquid is substantially faster than from the high-density liquid, and the enhanced fluctuations associated with critical points are also known to speed nucleation. High supercooling enhances nucleation, but the approaching glass transition should frustrate it. This complex interplay gives rise to unexpected behaviors in the rate of ice nucleation near the critical point. The seeding technique was used, in combination with classical nucleation theory, to estimate these rates in the (less computationally intensive) TIP4P/Ice model of water.