Abstract
This paper extends our earlier studies of free energy functions of density and crystalline order parameters for models of supercooled water, which allows us to examine the possibility of two distinct metastable liquid phases [D. T. Limmer and D. Chandler, J. Chem. Phys. 135, 134503 (2011) and preprint arXiv:1107.0337 (2011)]. Low-temperature reversible free energy surfaces of several different atomistic models are computed: mW water, TIP4P/2005 water, Stillinger-Weber silicon, and ST2 water, the last of these comparing three different treatments of long-ranged forces. In each case, we show that there is one stable or metastable liquid phase, and there is an ice-like crystal phase. The time scales for crystallization in these systems far exceed those of structural relaxation in the supercooled metastable liquid. We show how this wide separation in time scales produces an illusion of a low-temperature liquid-liquid transition. The phenomenon suggesting metastability of two distinct liquid phases is actually coarsening of the ordered ice-like phase, which we elucidate using both analytical theory and computer simulation. For the latter, we describe robust methods for computing reversible free energy surfaces, and we consider effects of electrostatic boundary conditions. We show that sensible alterations of models and boundary conditions produce no qualitative changes in low-temperature phase behaviors of these systems, only marginal changes in equations of state. On the other hand, we show that altering sampling time scales can produce large and qualitative non-equilibrium effects. Recent reports of evidence of a liquid-liquid critical point in computer simulations of supercooled water are considered in this light.
Highlights
This is our second paper examining whether molecular simulation provides support for the hypothesis that supercooled water possesses two distinct liquid phases with a reversible coexistence line ending at a critical point.[1]
In the first (Paper I),[2] we described our results for pertinent free energy functions of three different models: the mW model of water,[3] a variant of the ST2 model for water,[4] and the Stillinger-Weber model for Si.[5]
We see that the low-temperature behaviors of several different models of water-like liquids are similar
Summary
This is our second paper examining whether molecular simulation provides support for the hypothesis that supercooled water possesses two distinct liquid phases with a reversible coexistence line ending at a critical point.[1]. This limit can require simulation times thousands of times longer than those needed to equilibrate ρ Not accounting for this behavior can give the illusion of a reversible polyamorphism because the non-equilibrium free energy, −kBT ln[P (ρ|Q6) Pne(Q6, t)], can have a low-Q6 basin for times shorter than those required for Q6 to diffuse towards its equilibrium crystal value at high Q6. Crystallization following the melting of glass[33] and crystallization following the rapid quench of water into the liquid’s “no-man’s land”[34] are much like nonequilibrium dynamics evolving from low to high Q6 on the middle and left free energy surfaces pictured, an observation worthy of future study These interesting non-equilibrium processes and the transitions between different amorphous solids of water are not our focus in this work.
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