(208b) Free Energy Analysis of the Liquid-Liquid Transition in Supercooled ST2 Water

Many of the well-known thermodynamic anomalies of water, such as its negative thermal expansion and increased compressibility upon cooling, become more pronounced when it is cooled below its freezing point into a metastable liquid.  One thermodynamically consistent interpretation of water’s anomalies posits that water becomes highly compressible when cooled below its freezing point due to the presence of a second critical point associated with a first-order phase transition between two metastable liquid phases¹. Since the region of the phase diagram where this hypothetical critical point would occur is below the homogenous nucleation temperature of bulk water, obtaining direct experimental evidence to falsify the second critical point hypothesis has so far proved to be a significant challenge.

We examine the phase behavior of the ST2 water model² under deeply supercooled conditions, using state-of-the-art molecular simulation techniques  (umbrella sampling and well-tempered metadynamics) to compute the reversible free energy surface parameterized by density and bond-orientational order. Our analysis demonstrates that ST2 water phase-separates at sufficiently low temperatures, forming two liquid polymorphs that are metastable with respect to cubic ice. Such findings are consistent with our earlier umbrella sampling³ and grand canonical Monte Carlo⁴ calculations. The nature of the liquid-liquid phase transition is also investigated by examining the finite-size scaling behavior of the interfacial free energy between the two liquids.  We find that the interfacial free energy obeys the N^2/3 scaling law expected for a first-order transition, suggesting the existence of an associated second critical point in ST2 water.  Finally, we examine the mechanism for ice nucleation from the liquid state and discuss order parameters for describing this transition.

¹P. H. Poole, F. Sciortino, U. Essmann, and H. E. Stanley, Nature, 360, 324 (1992)

²F.H. Stillinger and A. Rahman, J Chem Phys, 60, 1545 (1974)

³Y. Liu, J. C. Palmer, A. Z. Panagiotopoulous and P. G. Debenedetti, J Chem Phys, 137, 214595 (2012)

 ⁴Y. Liu, A. Z. Panagiotopoulous and P. G. Debenedetti, J Chem Phys, 131, 104508 (2009).