We conduct extensive molecular dynamics computer simulations of two models for liquid silica [the model of Woodcock, Angell and Cheeseman, J. Phys. Chem. 65, 1565 (1976); and that of van Beest, Kramer, and van Santen, Phys. Rev. Lett. 64, 1955 (1990)] to determine their thermodynamic properties at low temperature T across a wide density range. We find for both models a wide range of states in which isochores of the potential energy U are a linear function of $T^{3/5},$ as recently proposed for simple liquids [Rosenfeld and P. Tarazona, Mol. Phys. 95, 141 (1998)]. We exploit this behavior to fit an accurate equation of state to our thermodynamic data. Extrapolation of this equation of state to low T predicts the occurrence of a liquid–liquid phase transition for both models. We conduct simulations in the region of the predicted phase transition, and confirm its existence by direct observation of phase separating droplets of atoms with distinct local density and coordination environments.

We report a numerical study, covering a wide range of packing fraction $\varphi$ and temperature $T$, for a system of particles interacting via a square well potential supplemented by an additional constraint on the maximum number $n_{\max }$ of bonded interactions. We show that, when $n_{\max }<6$, the liquid-gas coexistence region shrinks, giving access to regions of low $\varphi$ where dynamics can be followed down to low $T$ without an intervening phase separation. We characterize these arrested states at low densities (gel states) in terms of structure and dynamical slowing down, pointing out features which are very different from the standard glassy states observed at high $\varphi$ values.

We perform successive umbrella sampling grand canonical Monte Carlo computer simulations of the original ST2 model of water in the vicinity of the proposed liquid–liquid critical point, at temperatures above and below the critical temperature. Our results support the previous work of Y. Liu, A. Z. Panagiotopoulos and P. G. Debenedetti [J. Chem. Phys., 2009, 131, 104508], who provided evidence for the existence and location of the critical point for ST2 using the Ewald method to evaluate the long-range forces. Our results therefore demonstrate the robustness of the evidence for critical behavior with respect to the treatment of the electrostatic interactions. In addition, we verify that the liquid is equilibrated at all densities on the Monte Carlo time scale of our simulations, and also that there is no indication of crystal formation during our runs. These findings demonstrate that the processes of liquid-state relaxation and crystal nucleation are well separated in time. Therefore, the bimodal shape of the density of states, and hence the critical point itself, is a purely liquid-state phenomenon that is distinct from the crystal–liquid transition.

We carry out umbrella sampling Monte Carlo simulations to evaluate the free energy surface of the ST2 model of water as a function of two order parameters, the density and a bond-orientational order parameter. We approximate the long-range electrostatic interactions of the ST2 model using the reaction-field method. We focus on state points in the vicinity of the liquid-liquid critical point proposed for this model in earlier work. At temperatures below the predicted critical temperature we find two basins in the free energy surface, both of which have liquid-like bond orientational order, but differing in density. The pressure and temperature dependence of the shape of the free energy surface is consistent with the assignment of these two basins to the distinct low density and high density liquid phases previously predicted to occur in ST2 water.