The putative liquid-liquid transition is a liquid-solid transition in atomistic models of water. II.

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.