Phase diagram of the ST2 model of water

Crystallization and the liquid-liquid critical point in nonbonded modified-WAC models

For decades, it has been known that Liquid-Liquid Critical Points (LLCPs) can exist in one-component liquids, yet a comprehensive understanding of the conditions under which they arise remains elusive. To better comprehend the possible interplay between the LLCP and the crystalline phase, we conduct molecular dynamics simulations using the nonbonded family of modified-WAC (mWAC) models, which are known to exhibit a LLCP for certain parameter values. By comparing different versions of the mWAC model-those featuring a LLCP and those lacking one-we identify several key differences between the models relating to crystallization. Those models that do have a LLCP are found to have multiple stable crystalline phases, one of them being a solid-state ionic conductor similar to superionic ice. Moreover, we find that for models that do not have a LLCP, the liquid becomes a glass at a larger range of temperatures, possibly preventing the occurrence of a LLCP. Further studies are required to determine if these results are general or model-specific.

Melting points of water models: Current situation

By using the direct coexistence method, we have calculated the melting points of ice I h at normal pressure for three recently proposed water models, namely, TIP3P-FB, TIP4P-FB, and TIP4P-D. We obtained T m = 216 K for TIP3P-FB, T m = 242 K for TIP4P-FB, and T m = 247 K for TIP4P-D. We revisited the melting point of TIP4P/2005 and TIP5P obtaining T m = 250 and 274 K, respectively. We summarize the current situation of the melting point of ice I h for a number of water models and conclude that no model is yet able to simultaneously reproduce the melting temperature of ice I h and the temperature of the maximum in density at room pressure. This probably points toward our both still incomplete knowledge of the potential energy surface of water and the necessity of incorporating nuclear quantum effects to describe both properties simultaneously.

Evidence of a liquid-liquid phase transition in H[Formula: see text]O and D[Formula: see text]O from path-integral molecular dynamics simulations

We perform path-integral molecular dynamics (PIMD), ring-polymer MD (RPMD), and classical MD simulations of H[Formula: see text]O and D[Formula: see text]O using the q-TIP4P/F water model over a wide range of temperatures and pressures. The density [Formula: see text], isothermal compressibility [Formula: see text], and self-diffusion coefficients D(T) of H[Formula: see text]O and D[Formula: see text]O are in excellent agreement with available experimental data; the isobaric heat capacity [Formula: see text] obtained from PIMD and MD simulations agree qualitatively well with the experiments. Some of these thermodynamic properties exhibit anomalous maxima upon isobaric cooling, consistent with recent experiments and with the possibility that H[Formula: see text]O and D[Formula: see text]O exhibit a liquid-liquid critical point (LLCP) at low temperatures and positive pressures. The data from PIMD/MD for H[Formula: see text]O and D[Formula: see text]O can be fitted remarkably well using the Two-State-Equation-of-State (TSEOS). Using the TSEOS, we estimate that the LLCP for q-TIP4P/F H[Formula: see text]O, from PIMD simulations, is located at [Formula: see text] MPa, [Formula: see text] K, and [Formula: see text] g/cm[Formula: see text]. Isotope substitution effects are important; the LLCP location in q-TIP4P/F D[Formula: see text]O is estimated to be [Formula: see text] MPa, [Formula: see text] K, and [Formula: see text] g/cm[Formula: see text]. Interestingly, for the water model studied, differences in the LLCP location from PIMD and MD simulations suggest that nuclear quantum effects (i.e., atoms delocalization) play an important role in the thermodynamics of water around the LLCP (from the MD simulations of q-TIP4P/F water, [Formula: see text] MPa, [Formula: see text] K, and [Formula: see text] g/cm[Formula: see text]). Overall, our results strongly support the LLPT scenario to explain water anomalous behavior, independently of the fundamental differences between classical MD and PIMD techniques. The reported values of [Formula: see text] for D[Formula: see text]O and, particularly, H[Formula: see text]O suggest that improved water models are needed for the study of supercooled water.

Signatures of sluggish dynamics and local structural ordering during ice nucleation

We investigate the microscopic pathway of spontaneous crystallization in the ST2 model of water under deeply supercooled conditions via unbiased classical molecular dynamics simulations. After quenching below the liquid–liquid critical point, the ST2 model spontaneously separates into low-density liquid (LDL) and high-density liquid phases, respectively. The LDL phase, which is characterized by lower molecular mobility and enhanced structural order, fosters the formation of a sub-critical ice nucleus that, after a stabilization time, develops into the critical nucleus and grows. Polymorphic selection coincides with the development of the sub-critical nucleus and favors the formation of cubic (Ic) over hexagonal (Ih) ice. We rationalize polymorphic selection in terms of geometric arguments based on differences in the symmetry of second neighbor shells of ice Ic and Ih, which are posited to favor formation of the former. The rapidly growing critical nucleus absorbs both Ic and Ih crystallites dispersed in the liquid phase, a crystal with stacking faults. Our results are consistent with, and expand upon, recent observations of non-classical nucleation pathways in several systems.

Advances in the study of supercooled water

In this review, we report recent progress in the field of supercooled water. Due to its uniqueness, water presents numerous anomalies with respect to most simple liquids, showing polyamorphism both in the liquid and in the glassy state. We first describe the thermodynamic scenarios hypothesized for the supercooled region and in particular among them the liquid-liquid critical point scenario that has so far received more experimental evidence. We then review the most recent structural indicators, the two-state model picture of water, and the importance of cooperative effects related to the fact that water is a hydrogen-bonded network liquid. We show throughout the review that water's peculiar properties come into play also when water is in solution, confined, and close to biological molecules. Concerning dynamics, upon mild supercooling water behaves as a fragile glass former following the mode coupling theory, and it turns into a strong glass former upon further cooling. Connections between the slow dynamics and the thermodynamics are discussed. The translational relaxation times of density fluctuations show in fact the fragile-to-strong crossover connected to the thermodynamics arising from the existence of two liquids. When considering also rotations, additional crossovers come to play. Mobility-viscosity decoupling is also discussed in supercooled water and aqueous solutions. Finally, the polyamorphism of glassy water is considered through experimental and simulation results both in bulk and in salty aqueous solutions. Grains and grain boundaries are also discussed.

Dynamical crossover and its connection to the Widom line in supercooled TIP4P/Ice water

We perform molecular dynamics simulations with the TIP4P/Ice water model to characterize the relationship between dynamics and thermodynamics of liquid water in the supercooled region. We calculate the relevant properties of the phase diagram, and we find that TIP4P/Ice presents a retracing line of density maxima, similar to what was previously found for atomistic water models and models of other tetrahedral liquids. For this model, a liquid-liquid critical point between a high-density liquid and a low-density liquid was recently found. We compute the lines of the maxima of isothermal compressibility and the minima of the coefficient of thermal expansion in the one phase region, and we show that these lines point to the liquid-liquid critical point while collapsing on the Widom line. This line is the line of the maxima of correlation length that emanates from a second order critical point in the one phase region. Supercooled water was found to follow mode coupling theory and to undergo a transition from a fragile to a strong behavior right at the crossing of the Widom line. We find here that this phenomenology also happens for TIP4P/Ice. Our results appear, therefore, to be a general characteristic of supercooled water, which does not depend on the interaction potential used, and they reinforce the idea that the dynamical crossover from a region where the relaxation mechanism is dominated by cage relaxation to a region where cages are frozen and hopping dominates is correlated in water to a phase transition between a high-density liquid and a low-density liquid.

Glass polymorphism and liquid-liquid phase transition in aqueous solutions: experiments and computer simulations

One of the most intriguing anomalies of water is its ability to exist as distinct amorphous ice forms (glass polymorphism or polyamorphism). This resonates well with the possible first-order liquid-liquid phase transition (LLPT) in the supercooled state, where ice is the stable phase. In this Perspective, we review experiments and computer simulations that search for LLPT and polyamorphism in aqueous solutions containing salts and alcohols. Most studies on ionic solutes are devoted to NaCl and LiCl; studies on alcohols have mainly focused on glycerol. Less attention has been paid to protein solutions and hydrophobic solutes, even though they reveal promising avenues. While all solutions show polyamorphism and an LLPT only in dilute, sub-eutectic mixtures, there are differences regarding the nature of the transition. Isocompositional transitions for varying mole fractions are observed in alcohol but not in ionic solutions. This is because water can surround alcohol molecules either in a low- or high-density configuration whereas for ionic solutes, the water ion hydration shell is forced into high-density structures. Consequently, the polyamorphic transition and the LLPT are prevented near the ions, but take place in patches of water within the solutions. We highlight discrepancies and different interpretations within the experimental community as well as the key challenges that need consideration when comparing experiments and simulations. We point out where reinterpretation of past studies helps to draw a unified, consistent picture. In addition to the literature review, we provide original experimental results. A list of eleven open questions that need further consideration is identified.

Potential energy landscape of TIP4P/2005 water

We report a numerical study of the statistical properties of the potential energy landscape of TIP4P/2005, one of the most accurate rigid water models. We show that, in the region where equilibrated configurations can be generated, a Gaussian landscape description is able to properly describe the model properties. We also find that the volume dependence of the landscape properties is consistent with the existence of a locus of density maxima in the phase diagram. The landscape-based equation of state accurately reproduces the TIP4P/2005 pressure-vs-volume curves, providing a sound extrapolation of the free-energy at low T. A positive-pressure liquid-liquid critical point is predicted by the resulting free-energy.

Supercooled and glassy water: Metastable liquid(s), amorphous solid(s), and a no-man's land

We review the recent research on supercooled and glassy water, focusing on the possible origins of its complex behavior. We stress the central role played by the strong directionality of the water-water interaction and by the competition between local energy, local entropy, and local density. In this context we discuss the phenomenon of polyamorphism (i.e., the existence of more than one disordered solid state), emphasizing both the role of the preparation protocols and the transformation between the different disordered ices. Finally, we present the ongoing debate on the possibility of linking polyamorphism with a liquid-liquid transition that could take place in the no-man's land, the temperature-pressure window in which homogeneous nucleation prevents the investigation of water in its metastable liquid form.

What Determines the Ice Polymorph in Clouds?

Ice crystals in the atmosphere nucleate from supercooled liquid water and grow by vapor uptake. The structure of the ice polymorph grown has strong impact on the morphology and light scattering of the ice crystals, modulates the amount of water vapor in ice clouds, and can impact the molecular uptake and reactivity of atmospheric aerosols. Experiments and molecular simulations indicate that ice nucleated and grown from deeply supercooled liquid water is metastable stacking disordered ice. The ice polymorph grown from vapor has not yet been determined. Here we use large-scale molecular simulations to determine the structure of ice that grows as a result of uptake of water vapor in the temperature range relevant to cirrus and mixed-phase clouds, elucidate the molecular mechanism of the formation of ice at the vapor interface, and compute the free energy difference between cubic and hexagonal ice interfaces with vapor. We find that vapor deposition results in growth of stacking disordered ice only under conditions of extreme supersaturation, for which a nonequilibrium liquid layer completely wets the surface of ice. Such extreme conditions have been used to produce stacking disordered frost ice in experiments and may be plausible in the summer polar mesosphere. Growth of ice from vapor at moderate supersaturations in the temperature range relevant to cirrus and mixed-phase clouds, from 200 to 260 K, produces exclusively the stable hexagonal ice polymorph. Cubic ice is disfavored with respect to hexagonal ice not only by a small penalty in the bulk free energy (3.6 ± 1.5 J mol(-1) at 260 K) but also by a large free energy penalty at the ice-vapor interface (89.7 ± 12.8 J mol(-1) at 260 K). The latter originates in higher vibrational entropy of the hexagonal-terminated ice-vapor interface. We predict that the free energy penalty against the cubic ice interface should decrease strongly with temperature, resulting in some degree of stacking disorder in ice grown from vapor in the tropical tropopause layer, and in polar stratospheric and noctilucent clouds. Our findings support and explain the evolution of the morphology of ice crystals from hexagonal to trigonal symmetry with decreasing temperature, as reported by experiments and in situ measurements in clouds. We conclude that selective growth of the elusive cubic ice polymorph by manipulation of the interfacial properties can likely be achieved at the ice-liquid interface but not at the ice-vapor interface.

Free energy contributions and structural characterization of stacking disordered ices

Crystallization of ice from deeply supercooled water and amorphous ices - a process of fundamental importance in the atmosphere, interstellar space, and cryobiology - results in stacking disordered ices with a wide range of metastabilities with respect to hexagonal ice. The structural origin of this high variability, however, has not yet been elucidated. Here we use molecular dynamics simulations with the mW water model to characterize the structure of ice freshly grown from supercooled water at temperatures from 210 to 270 K, the thermodynamics of stacking faults, line defects, and interfaces, and to elucidate the interplay between kinetics and thermodynamics in determining the structure of ice. In agreement with experiments, the ice grown in the simulations is stacking disordered with a random distribution of cubic and hexagonal layers, and a cubicity that decreases with growth temperature. The former implies that the cubicity of ice is determined by processes at the ice/liquid interface, without memory of the structure of buried ice layers. The latter indicates that the probability of building a cubic layer at the interface decreases upon approaching the melting point of ice, which we attribute to a more efficient structural equilibration of ice at the liquid interface as the driving force for growth wanes. The free energy cost for creating a pair of cubic layers in ice is 8.0 J mol(-1) in experiments, and 9.7 ± 1.9 J mol(-1) for the mW water model. This not only validates the simulations, but also indicates that dispersion in cubicity is not sufficient to explain the large energetic variability of stacking disordered ices. We compute the free energy cost of stacking disorder, line defects, and interfaces in ice and conclude that a characterization of the density of these defects is required to predict the degree of metastability and vapor pressure of atmospheric ices.

Tuning the Liquid-Liquid Transition by Modulating the Hydrogen-Bond Angular Flexibility in a Model for Water

We propose a simple extension of the well known ST2 model for water [F. H. Stillinger and A. Rahman, J. Chem. Phys. 60, 1545 (1974)] that allows for a continuous modification of the hydrogen-bond angular flexibility. We show that the bond flexibility affects the relative thermodynamic stability of the liquid and of the hexagonal (or cubic) ice. On increasing the flexibility, the liquid-liquid critical point, which in the original ST2 model is located in the no-man's land (i.e., the region where ice is the thermodynamically stable phase) progressively moves to a temperature where the liquid is more stable than ice. Our study definitively proves that the liquid-liquid transition in the ST2 model is a genuine phenomenon, of high relevance in all tetrahedral network-forming liquids, including water.