The ability of several water models to predict the properties of ices is discussed. The emphasis is put on the results for the densities and the coexistence curves between the different ice forms. It is concluded that none of the most commonly used rigid models is satisfactory. A new model specifically designed to cope with solid-phase properties is proposed. The parameters have been obtained by fitting the equation of state and selected points of the melting lines and of the coexistence lines involving different ice forms. The phase diagram is then calculated for the new potential. The predicted melting temperature of hexagonal ice (Ih) at 1 bar is 272.2 K. This excellent value does not imply a deterioration of the rest of the properties. In fact, the predictions for both the densities and the coexistence curves are better than for TIP4P, which previously yielded the best estimations of the ice properties.

Abstract. In this review we focus on the determination of phase diagrams by computer simulation with particular attention to the fluid-solid and solid-solid equilibria. The methodology to compute the free energy of solid phases will be discussed. In particular, the Einstein crystal and Einstein molecule methodologies are described in a comprehensive way. It is shown that both methodologies yield the same free energies and that free energies of solid phases present noticeable finite size effects. In fact this is the case for hard spheres in the solid phase. Finite size corrections can be introduced, although in an approximate way, to correct for the dependence of the free energy on the size of the system. The computation of free energies of solid phases can be extended to molecular fluids. The procedure to compute free energies of solid phases of water (ices) will be described in detail. The free energies of ices Ih, II, III, IV, V, VI, VII, VIII, IX, XI and XII will be presented for the SPC/E and TIP4P models of water. Initial coexistence points leading to the determination of the phase diagram of water for these two models will be provided. Other methods to estimate the melting point of a solid, as the direct fluid-solid coexistence or simulations of the free surface of the solid will be discussed. It will be shown that the melting points of ice Ih for several water models, obtained from free energy calculations, direct coexistence simulations and free surface simulations, agree within their statistical uncertainty. Phase diagram calculations can indeed help to improve potential models of molecular fluids. For instance, for water, the potential model TIP4P/2005 can be regarded as an improved version of TIP4P. Here we will review some recent work on the phase diagram of the simplest ionic model, the restricted primitive model. Although originally devised to describe ionic liquids, the model is becoming quite popular to describe the behaviour of charged colloids. Besides the possibility of obtaining fluid-solid equilibria for simple protein models will be discussed. In these primitive models, the protein is described by a spherical potential with certain anisotropic bonding sites (patchy sites).

The melting temperature of ice I(h) for several commonly used models of water (SPC, SPC/E,TIP3P,TIP4P, TIP4P/Ew, and TIP5P) is obtained from computer simulations at p = 1 bar. Since the melting temperature of ice I(h) for the TIP4P model is now known [E. Sanz, C. Vega, J. L. F. Abascal, and L. G. MacDowell, Phys. Rev. Lett. 92, 255701 (2004)], it is possible to use the Gibbs-Duhem methodology [D. Kofke, J. Chem. Phys. 98, 4149 (1993)] to evaluate the melting temperature of ice I(h) for other potential models of water. We have found that the melting temperatures of ice I(h) for SPC, SPC/E, TIP3P, TIP4P, TIP4P/Ew, and TIP5P models are T = 190 K, 215 K, 146 K, 232 K, 245 K, and 274 K, respectively. The relative stability of ice I(h) with respect to ice II for these models has also been considered. It turns out that for SPC, SPC/E, TIP3P, and TIP5P the stable phase at the normal melting point is ice II (so that ice I(h) is not a thermodynamically stable phase for these models). For TIP4P and TIP4P/Ew, ice I(h) is the stable solid phase at the standard melting point. The location of the negative charge along the H-O-H bisector appears as a critical factor in the determination of the relative stability between the I(h) and II ice forms. The methodology proposed in this paper can be used to investigate the effect upon a coexistence line due to a change in the potential parameters.

The phase diagram of water as obtained from computer simulations is presented for the first time for two of the most popular models of water, TIP4P and SPC/E. This Letter shows that the prediction of the phase diagram is an extremely stringent test for any water potential function, and that it may be useful in developing improved potentials. The TIP4P model provides a qualitatively correct description of the phase diagram, unlike the SPC/E model which fails in this purpose. New behavior not yet observed experimentally is predicted by the simulations: the existence of metastable reentrant behavior in the melting curves of the low density ices (I,III,V) such that it could be possible to transform them into amorphous phases by adequate changes in pressure.

Among all of the freezing transitions, that of water into ice is probably the most relevant to biology, physics, geology, or atmospheric science. In this work, we investigate homogeneous ice nucleation by means of computer simulations. We evaluate the size of the critical cluster and the nucleation rate for temperatures ranging between 15 and 35 K below melting. We use the TIP4P/2005 and the TIP4P/ice water models. Both give similar results when compared at the same temperature difference with the model's melting temperature. The size of the critical cluster varies from ∼8000 molecules (radius = 4 nm) at 15 K below melting to ∼600 molecules (radius = 1.7 nm) at 35 K below melting. We use Classical Nucleation Theory (CNT) to estimate the ice-water interfacial free energy and the nucleation free-energy barrier. We obtain an interfacial free energy of 29(3) mN/m from an extrapolation of our results to the melting temperature. This value is in good agreement both with experimental measurements and with previous estimates from computer simulations of TIP4P-like models. Moreover, we obtain estimates of the nucleation rate from simulations of the critical cluster at the barrier top. The values we get for both models agree within statistical error with experimental measurements. At temperatures higher than 20 K below melting, we get nucleation rates slower than the appearance of a critical cluster in all water of the hydrosphere during the age of the universe. Therefore, our simulations predict that water freezing above this temperature must necessarily be heterogeneous.

We present a study of homogeneous crystal nucleation from metastable fluids via the seeding technique for four different systems: mW water, Tosi-Fumi NaCl, Lennard-Jones, and Hard Spheres. Combining simulations of spherical crystal seeds embedded in the metastable fluid with classical nucleation theory, we are able to successfully describe the nucleation rate for all systems in a wide range of metastability. The crystal-fluid interfacial free energy extrapolated to coexistence conditions is also in good agreement with direct calculations of such parameter. Our results show that seeding is a powerful technique to investigate crystal nucleation.

We study by molecular dynamics the interplay between arrest and crystallization in hard spheres. For state-points in the plane of volume fraction (0.54 ≤ φ ≤ 0.63) and polydispersity (0 ≤ s ≤ 0.085), we delineate states that spontaneously crystallize from those that do not. For non-crystallising (or pre-crystallization) samples we find isodiffusivity lines consistent with an ideal glass transition at φg ≈ 0.585, independent of s. Despite this, for s < 0.05, crystallization occurs at φ > φg. This happens on timescales for which the system is ageing, and a diffusive regime in the mean square displacement is not reached; by those criteria, the system is a glass. Hence, contrary to a widespread assumption in the colloid literature, occurrence of spontaneous crystallization within a bulk amorphous state does not prove that this state was an ergodic fluid rather than a glass.PACS numbers: 64.70. Pf, 61.20.Lc, 82.70.Dd Pioneering computer simulations in the 1950s predicted that a system of monodisperse hard spheres (HS) should crystallize at high enough volume fraction, φ [1]. Thirty years later, a full phase diagram (from fluid densities up to random close packing, φ RCP ≈ 0.64) was measured in a suspension of hard-sphere PMMA colloids [2]. Alongside the fluid and crystal phases, this reported the formation of a glass at φ ≥ φ g ≈ 0.58 [2,3]. The existence and nature of the HS glass remains controversial [4,5,6,7]: for instance, a recent report [8] suggests that HS suspensions remain ergodic well beyond φ = 0.58. Ergodicity depends on observation time, so this finding does not rule out colloidal glasses on timescales of several hours. (It does rule out an ideal glass transition, in which the structural relaxation time for φ > φ g is strictly infinite, as predicted by mode-coupling theory (MCT) [9].) For many years, a number of colloid physicists have held that, because particles in a glass cannot rearrange diffusively, crystallization within a homogeneous bulk glass cannot proceed unless it is seeded with pre-formed nuclei [10]. This view is stated explicitly in [4] (but see [11]); in combination with the observation that hard sphere colloids at φ > φ g show rapid bulk crystallization in microgravity, it has led Chaikin and others to assert that such colloids do not have a glass transition at all [12].An important factor in studies of all these phenomena is polydispersity. Fractional standard deviations in particle size, s, of a few percent are inevitable experimentally. Some authors hold that polydispersity is essential to the formation of a hard sphere glass [13,14] because a putative monodisperse sample would crystallize too rapidly [15]. (Here, as for glasses generally, the contest between vitrification and crystallization is usually portrayed as happening during rather than after a quench [16].) In colloids, polydispersity could play two distinct roles. First, it might influence cage formation, shifting any glass transition point. However, computational [17, 18] and experimental [19] work seems to suggest tha...

In this work, we evaluate by means of computer simulations the rate for ice homogeneous nucleation for several water models such as TIP4P, TIP4P/2005,TIP4P/ICE, and mW (following the same procedure as in Sanz et al. [J. Am. Chem. Soc. 135, 15008 (2013)]) in a broad temperature range. We estimate the ice-liquid interfacial free-energy, and conclude that for all water models γ decreases as the temperature decreases. Extrapolating our results to the melting temperature, we obtain a value of the interfacial free-energy between 25 and 32 mN/m in reasonable agreement with the reported experimental values. Moreover, we observe that the values of γ depend on the chosen water model and this is a key factor when numerically evaluating nucleation rates, given that the kinetic prefactor is quite similar for all water models with the exception of the mW (due to the absence of hydrogens). Somewhat surprisingly the estimates of the nucleation rates found in this work for TIP4P/2005 are slightly higher than those of the mW model, even though the former has explicit hydrogens. Our results suggest that it may be possible to observe in computer simulations spontaneous crystallization of TIP4P/2005 at about 60 K below the melting point.