Multiple liquid–liquid transitions in supercooled water

Water: A Tale of Two Liquids

Water is the most abundant liquid on earth and also the substance with the largest number of anomalies in its properties. It is a prerequisite for life and as such a most important subject of current research in chemical physics and physical chemistry. In spite of its simplicity as a liquid, it has an enormously rich phase diagram where different types of ices, amorphous phases, and anomalies disclose a path that points to unique thermodynamics of its supercooled liquid state that still hides many unraveled secrets. In this review we describe the behavior of water in the regime from ambient conditions to the deeply supercooled region. The review describes simulations and experiments on this anomalous liquid. Several scenarios have been proposed to explain the anomalous properties that become strongly enhanced in the supercooled region. Among those, the second critical-point scenario has been investigated extensively, and at present most experimental evidence point to this scenario. Starting from very low temperatures, a coexistence line between a high-density amorphous phase and a low-density amorphous phase would continue in a coexistence line between a high-density and a low-density liquid phase terminating in a liquid–liquid critical point, LLCP. On approaching this LLCP from the one-phase region, a crossover in thermodynamics and dynamics can be found. This is discussed based on a picture of a temperature-dependent balance between a high-density liquid and a low-density liquid favored by, respectively, entropy and enthalpy, leading to a consistent picture of the thermodynamics of bulk water. Ice nucleation is also discussed, since this is what severely impedes experimental investigation of the vicinity of the proposed LLCP. Experimental investigation of stretched water, i.e., water at negative pressure, gives access to a different regime of the complex water diagram. Different ways to inhibit crystallization through confinement and aqueous solutions are discussed through results from experiments and simulations using the most sophisticated and advanced techniques. These findings represent tiles of a global picture that still needs to be completed. Some of the possible experimental lines of research that are essential to complete this picture are explored.

On the behavior of water at subfreezing temperatures in a protein crystal: evidence of higher mobility than in bulk water

NMR experiments have shown that water molecules in the crystal of the protein Crh are still mobile at temperatures well below 273 K. In order to investigate this water anomaly, a molecular dynamics (MD) simulation study of crystalline Crh was carried out to determine the mobility of water in this crystal. The simulations were carried out at three temperatures, 150, 200, and 291 K. Simulations of bulk water at these temperatures were also done to obtain the properties of the simple point charge (SPC) water model used at these temperatures and to allow a comparison of the properties of water in the Crh crystal with those of bulk water at the same temperatures. According to the simulations, water is immobilized at 150 K both in crystal and in bulk water. As expected, at 291 K it diffuses and rotates more slowly in the protein crystal than in bulk water. However, at 200 K, the translational and rotational mobility of the water molecules is larger in the crystal than in bulk water. The enhancement of water mobility in the crystal at 200 K was further investigated by MD simulations in which the backbone or all protein atoms were positionally restrained, and in which additionally the electrostatic protein-water interactions were removed. Of these changes in the environment of the water molecules, rigidifying the protein backbones slightly enhanced water diffusion, while it slowed down rotation. In contrast, removal of electrostatic protein-water interactions did not change water diffusion but enhanced rotational motion significantly. Further investigations are required to delineate particular features of the protein crystal that induce the anomalous behavior of water at 200 K.

Interplay of the glass transition and the liquid-liquid phase transition in water

Water has multiple glassy states, often called amorphous ices. Low-density (LDA) and high-density (HDA) amorphous ice are separated by a dramatic, first-order like phase transition. It has been argued that the LDA-HDA transformation connects to a first-order liquid-liquid phase transition (LLPT) above the glass transition temperature T(g). Direct experimental evidence of the LLPT is challenging to obtain, since the LLPT occurs at conditions where water rapidly crystallizes. In this work, we explore the implications of a LLPT on the pressure dependence of T(g)(P) for LDA and HDA by performing computer simulations of two water models - one with a LLPT, and one without. In the absence of a LLPT, T(g)(P) for all glasses nearly coincide. When there is a LLPT, different glasses exhibit dramatically different T(g)(P) which are directly linked with the LLPT. Available experimental data for T(g)(P) are only consistent with the scenario including a LLPT.

On the isobaric thermal expansivity of liquids

The temperature and pressure dependence of isobaric thermal expansivity, α(p), in liquids is discussed in this paper. Reported literature data allow general trends in this property that are consistent with experimental evidence to be established. Thus, a negative pressure dependence is to be expected except around the critical point. On the other hand, α(p) exhibits broad regions of negative and positive temperature dependence in the (T, p) plane depending on the nature of the particular liquid. These trends are rationalized here in terms of various molecular-based equations of state. The analysis of the Lennard-Jones, hard sphere square well and restricted primitive model equations allows understanding the differences in the α(p) behavior between liquids of diverse chemical nature (polar, nonpolar, and ionic): broader regions of negative temperature and positive pressure dependencies are obtained for liquids characterized by larger ranges of the interparticle potential. Also, using the statistical associating fluid theory (SAFT) allowed the behavior of more complex systems (basically, those potentially involving chain and association effects) to be described. The effect of chain length is rather simple: increasing it is apparently equivalent to raise the interaction range. By contrast, association presents a quite complex effect on α(p), which comes from a balance between the dispersive and associative parts of the interaction potential. Thus, if SAFT parameters are adjusted to obtain low association ability, α(p) is affected by each mechanism at clearly separate regions, one at low temperature, due to association, and the other to dispersive forces, which has its origin in fluctuations related with vapor-liquid transition.

Widom line and the liquid-liquid critical point for the TIP4P/2005 water model

The Widom line and the liquid-liquid critical point of water in the deeply supercooled region are investigated via computer simulation of the TIP4P/2005 model. The Widom line has been calculated as the locus of compressibility maxima. It is quite close to the experimental homogeneous nucleation line and, in the region studied, it is almost parallel to the curve of temperatures of maximum density at fixed pressure. The critical temperature is determined by examining which isotherm has a region with flat slope. An interpolation in the Widom line gives the rest of the critical parameters. The computed critical parameters are T(c)=193 K, p(c)=1350 bar, and ρ(c)=1.012 g/cm(3). Given the performance of the model for the anomalous properties of water and for the properties of ice phases, the calculated critical parameters are probably close to those of real water.

Dynamical properties of supercooled water close to the liquid-liquid coexistence lines, and their relation to those at ambient conditions

We report results of molecular dynamics simulations of supercooled bulk water at 180 K, close to the liquid/liquid coexistence lines recently discovered in the supercooled regime, both experimentally and by computer simulations. Despite the considerable differences in the densities of the three states considered, the obtained velocity autocorrelation functions display very similar behaviour in every case. On the other hand, the corresponding spectra show the presence of three well-defined modes. The two modes at higher frequencies are assigned to the symmetric and asymmetric stretching motions, respectively, whereas the lowest frequency mode to the bending and torsional motions in clusters of five hydrogen-bonded water molecules. A careful fitting procedure demonstrates the presence of such clusters also in the normal liquid phase of water at ambient conditions.

Heterogeneities in confined water and protein hydration water

We report recent efforts to understand a broad range of experiments on confined water and protein hydration water, many initiated by a collaboration between workers at the University of Messina and MIT-the editors of this special issue. Preliminary calculations are not inconsistent with one tentative interpretation of these experiments as resulting from the system passing from the high-temperature high-pressure 'HDL' side of the Widom line (where the liquid might display non-Arrhenius behavior) to the low-temperature low-pressure 'LDL' side of the Widom line (where the liquid might display Arrhenius behavior). The Widom line-defined to be the line in the pressure-temperature plane where the correlation length has its maximum-arises if there is a critical point. Hence, interpreting the Messina-MIT experiments in terms of a Widom line is of potential relevance to testing, experimentally, the hypothesis that water displays a liquid-liquid critical point.

Molecular Dynamics Simulations on the Glass-to-liquid Transition in High Density Amorphous Ice

It is an open question whether high density amorphous (HDA) ice is a glassy material structurally related to an ultraviscous high density liquid (HDL) or a nanocrystalline material unrelated to a liquid. In order to shed light on this question we have performed molecular dynamics simulations on a HDA model system at a pressure of p ≈ 0.3 GPa using the COMPASS force field. After removing the irreversible structural relaxation effect by initial isobaric heating/cooling cycles, we observe a deviation from linearity in the density vs. temperature plot in the range 170 ± 15 K in subsequent cycles, which we attribute to the glass-transition temperature T g. This assignment of T g is corroborated by two independent methods, namely from a rapid increase in the diffusion coefficient at ≈169 K and a deviation from linearity at ≈174 K in an enthalpy versus temperature plot. The structure of the model system is in good agreement with the experimentally determined structure of HDA. We, thus, suggest that HDA may indeed be a low temperature structural proxy of an ultraviscous liquid HDL.

Transient Pronounced Density Variation in Amorphous Ice Structures

The structural transformation of different high-density amorphous (HDA) ice modifications into the low-density amorphous (LDA) ice is studied by small-angle neutron scattering (SANS) techniques. All experiments have been performed at stationary conditions allowing to collect detailed information not only on the SANS formfactor but also on its time evolution and, hence, the kinetics governing the transformation process. A parametrization of the SANS formfactor by a superposition of the Debye-Bueche formfactor, characterizing a non-particulate two phase mixture, and a Porod-limit scattering formfactor is carried out successfully. The Porod-limit scattering indicates the presence of sharp interfaces and surfaces present in the sample material. Interpreting this signal as due to a grainy consistency of the amorphous samples grain sizes of the order of at least some micrometers can be approximated. The Debye-Bueche ansatz accounts for the formation of a transient pronounced signal on mesoscopic length scales. Its analysis results in an average domain size of 12–16 Å characterizing a hypothetical two phase mixture in its state of strongest intermixture, i.e., strongest heterogeneity. Interpretation of the Debye-Bueche formfactor by the Porod invariant results in a sample contrast that is by a factor of about 4 smaller than a hypothetical first-order transition between any modification of HDA and LDA. This statement is valid for an unstrained two-phase system separated by sharp interfaces. A detailed discussion is given which tries to set the present results into a more realistic context.

Homogeneous Ice Nucleation in Water and Aqueous Solutions

This review provides an introduction to ice nucleation processes in supercooled water and aqueous solutions. Concepts for experimental techniques suitable to study homogeneous ice nucleation are addressed, in particular differential scanning calorimetry of inverse emulsions. Ice nucleation data from aqueous solutions have been analyzed using two approaches, and the interrelations between those are examined. It is argued that the ice nucleation process is driven entirely by thermodynamic quantities and how this can be understood in the context of three proposed theories for supercooled liquid water. Ice nucleation data for pure water droplets surrounded by a gas have been compiled and evaluated; within experimental uncertainty neither a volume dependent nucleation process nor a surface dependent nucleation process is convincingly supported by the analysis. Finally, open questions in the area of supercooled aqueous solutions and ice nucleation are discussed.

High-density amorphous ice: Molecular dynamics simulations of the glass transition at 0.3 GPa

Based on several force fields (COMPASS, modified TIP3P and SPC/E) high-density amorphous ice is simulated by use of isothermal-isobaric molecular dynamics at a pressure of p approximately 0.3 GPa in the temperature range from 70 to 300 K. Starting at low temperature a large number of heating/cooling cycles are performed and several characteristic properties (density, total energy, and mobility) are traced as functions of temperature. While the first cycles are showing irreversible structural relaxation effects data points from further cycles are reproducible and give clear evidence for the existence of a glass-to-liquid transition. Although, the observed transition temperatures T(g) are dependent on the actual force field used and slightly dependent on the method adopted the results indicate that high-density amorphous ices may indeed be low-temperature structural proxies of ultraviscous high-density liquids.

Liquid water and ices: understanding the structure and physical properties

A review of the structure and some properties of condensed phases of water is given. Since the discovery of the polymorphism of crystalline ice (beginning of the twentieth century), 15 ice modifications have been found and their structures have been determined. If we do not take into consideration proton ordering or disordering, nine distinct crystalline ice modifications in which water molecules retain their individuality are known. In the tenth, ice X, there are no H(2)O molecules. It contains ions (or atoms) of oxygen and hydrogen. The structure of all these modifications is described and information about their fields of stability and about the transition between them is given. It is emphasized that there are ice modifications which are metastable at any temperature and pressure (ices Ic, IV and XII), and many modifications can exist as metastable phases beyond their fields of stability. The ability of water to exist in metastable states is one of its remarkable properties. Several amorphous ice modifications (all of them are metastable) are known. Brief information about their properties and transitions between them is given. At the end of the 1960s the conception of the water structure as a three-dimensional hydrogen-bonded network was conclusively formed. Discovery of the polymorphism of amorphous ices awakened interest in the heterogeneity of the water network. Structural and dynamical heterogeneity of liquid water is discussed in detail. Computer simulation showed that the diffusion coefficient of water molecules in dense regions of the network is lower than in the loose regions, while an increase of density of the entire network gives rise to an increase of diffusion coefficient. This finding contradicts the conceptions associated with the primitive two-state models and can be explained from pressure dependences of melting temperature and of homogeneous nucleation temperature. A brief discussion of the picture of molecular motions in liquid water based on experiment and on computer simulation is given. This picture is still very incomplete. The most fascinating idea that was put forward during the last 20 years was the second critical point conjecture. It is still not clear whether this conjecture corresponds to reality.

Interpenetration as a mechanism for liquid-liquid phase transitions

We study simple lattice systems to demonstrate the influence of interpenetrating bond networks on phase behavior. We promote interpenetration by using a Hamiltonian with a weakly repulsive interaction with nearest neighbors and an attractive interaction with second-nearest neighbors. In this way, bond networks will form between second-nearest neighbors, allowing for two (locally) distinct networks to form. We obtain the phase behavior from analytic solution in the mean-field approximation and exact solution on the Bethe lattice. We compare these results with exact numerical results for the phase behavior from grand canonical Monte Carlo simulations on square, cubic, and tetrahedral lattices. All results show that these simple systems exhibit rich phase diagrams with two fluid-fluid critical points and three thermodynamically distinct phases. We also consider including third-nearest-neighbor interactions, which give rise to a phase diagram with four critical points and five thermodynamically distinct phases. Thus the interpenetration mechanism provides a simple route to generate multiple liquid phases in single-component systems, such as hypothesized in water and observed in several model and experimental systems. Additionally, interpenetration of many such networks appears plausible in a recently considered material made from nanoparticles functionalized by single-strands of DNA.

Spectral statistics of the quenched normal modes of a network-forming molecular liquid

We evaluate the density of states of the quenched normal modes of ST2 water, and their statistical fluctuations, for a range of densities spanning three regimes of behavior of a hydrogen bonded liquid: a lower-density regime of random tetrahedral network formation, in the vicinity of a liquid-liquid critical point, and in a higher-density regime of fragile glass-forming behavior. For all cases we find that the fluctuations around the mean spectral densities obey the predictions of the Gaussian orthogonal ensemble of random matrix theory. We also measure the participation ratio of the normal modes across the entire frequency range, and find behavior consistent with the majority of modes being of an extended nature, rather than localized.

Hierarchies of networked phases induced by multiple liquid-liquid critical points

Nanoparticles and colloids functionalized by four single strands of DNA can be thought of as designed analogs to tetrahedral network-forming atoms and molecules, with a difference that the attached DNA strands allow for control of the length scale of bonding relative to the core size. We explore the behavior of an experimentally realized model for nanoparticles functionalized by four single strands of DNA (a tetramer), and show that this single-component model exhibits a rich phase diagram with at least three critical points and four thermodynamically distinct amorphous phases. We demonstrate that the additional critical points are part of the Ising universality class, like the ordinary liquid-gas critical point. The dense phases consist of a hierarchy of interpenetrating networks, reminiscent of a woven cloth. Thus, bonding specificity of DNA provides an effective route to generate new nano-networked materials with polyamorphic behavior. The concept of network interpenetration helps to explain the generation of multiple liquid phases in single-component systems, suggested to occur in some atomic and molecular network-forming fluids, including water and silica.

Structural and thermodynamic properties of different phases of supercooled liquid water

Computer simulation results are reported for a realistic polarizable potential model of water in the supercooled region. Three states, corresponding to the low density amorphous ice, high density amorphous ice, and very high density amorphous ice phases are chosen for the analyses. These states are located close to the liquid-liquid coexistence lines already shown to exist for the considered model. Thermodynamic and structural quantities are calculated, in order to characterize the properties of the three phases. The results point out the increasing relevance of the interstitial neighbors, which clearly appear in going from the low to the very high density amorphous phases. The interstitial neighbors are found to be, at the same time, also distant neighbors along the hydrogen bonded network of the molecules. The role of these interstitial neighbors has been discussed in connection with the interpretation of recent neutron scattering measurements. The structural properties of the systems are characterized by looking at the angular distribution of neighboring molecules, volume and face area distribution of the Voronoi polyhedra, and order parameters. The cumulative analysis of all the corresponding results confirms the assumption that a close similarity between the structural arrangement of molecules in the three explored amorphous phases and that of the ice polymorphs I(h), III, and VI exists.

Absence of a diffusion anomaly of water in the direction perpendicular to hydrophobic nanoconfining walls

We perform molecular dynamics simulations to investigate the diffusive motion of TIP5P (the transferable intermolecular potential with five points) water in the direction perpendicular to the two hydrophobic confining walls. To calculate the diffusion constant, we use the concept of the characteristic residence time which is calculated from the exponential decay of the residence time probability density function. We find that a diffusion anomaly, increase of diffusion upon compression, is absent in the direction perpendicular to the confining walls down to the lowest temperature we simulate, 220K , whereas there is a diffusion anomaly, similar to that in bulk water, in the direction parallel to the walls. The absence of a diffusion anomaly in the direction perpendicular to the walls may arise mainly due to nanoconfinement, rather than due to the hydrophobic property of the confining walls. In addition, we find that the temperature dependence of the diffusion constant along the constant density path in the perpendicular direction shows a Vogel-Fulcher-Tammann form.

Structure of coexisting liquid phases of supercooled water: Analogy with ice polymorphs

The structural changes occurring in supercooled liquid water upon moving from one coexisting liquid phase to the other have been investigated by computer simulation using a polarizable interaction potential model. The obtained results favorably compare with recent neutron scattering data of high and low density water. In order to assess the physical origin of the observed structural changes, computer simulation of several ice polymorphs has also been carried out. Our results show that there is a strict analogy between the structure of various disordered (supercooled) and ordered (ice) phases of water, suggesting that the occurrence of several different phases of supercooled water is rooted in the same physical origin that is responsible for ice polymorphism.

Effect of confinement on the liquid-liquid phase transition of supercooled water

We report on an observation of the phase transition between two liquid phases of supercooled confined water in simulations. The temperature of the liquid-liquid transition of water at zero pressure slightly decreases due to confinement in the hydrophobic pore. The hydrophilic confinement affects this temperature in the opposite direction and shifts the critical point of the liquid-liquid transition to a higher pressure. As a result, in a strongly hydrophilic pore the liquid-liquid phase transition becomes continuous at zero pressure, indicating the shift of its critical point from negative to a positive pressure. These findings indicate that experimental studies of water confined in the pores of various hydrophobicity/hydrophilicity may clarify the location of the liquid-liquid critical point of bulk water.

Fluid-phase behavior of binary mixtures in which one component can have two critical points

We investigate theoretically the binary fluid-phase behavior of mixtures in which one water-like component can have two critical points. We consider three equal-sized nonpolar solutes that differ in the strength of their dispersive interactions (a1 < a2 < a3, where a denotes the van der Waals attractive parameter). In each case, we compare the phase behavior predicted using two sets of parameters for water: one giving rise to a pure component low-temperature liquid-liquid transition terminating at a critical point (two-critical-point parameter set), and one in which no such second critical point exists (singularity-free parameter set). Regardless of the parameter values used, we find five mixture critical lines. Using the two-critical-point parameter set, we find that a critical line originates at water's second critical point for aqueous mixtures involving solutes 1, 2, or 3. For mixtures involving solutes 1 or 2, this line extends towards low pressures and high temperatures as the solute mole fraction increases, and is closely related to the critical line originating at water's ordinary vapor-liquid critical point: these two critical lines are loci of upper and lower consolute points corresponding to the same liquid-liquid transition. In mixtures involving solute 2, the critical locus emanating from water's second critical point is shifted to higher temperatures compared to mixtures involving solute 1, and extends up to T approximately 310 K at moderate pressures (ca. 200 bars). This suggests the possibility of an experimentally accessible manifestation of the existence of a second critical point in water. For binary mixtures involving solutes 1 or 2, changing the water parameters from the two critical points to the singularity-free case causes the disappearance of a lower consolute point at moderate pressures. For binary mixtures involving solute 3, the differences between two-critical-point and singularity-free behaviors occur only in the experimentally difficult-to-probe low-temperature and high-pressure region.

Phase-ordering kinetics of the liquid-liquid transition in single-component molecular liquids

Recently it has been revealed that even a single-component liquid can have more than two liquid states. The transition between these liquid states is called the "liquid-liquid transition." Most known liquid-liquid transitions occur at temperatures and pressures which are difficult to access experimentally, so the physical nature of the transition, particularly the kinetics, has remained elusive. However, the recent discovery of liquid-liquid transitions in molecular liquids opens up a possibility to study the kinetics in detail. Here, we report the first phase field simulation on the kinetics of a liquid-liquid transition and its direct comparison with experimental results of the molecular liquids. Both nucleation-growth-type and spinodal-decomposition-type liquid-liquid transformation observed experimentally are well reproduced by numerical simulation based on a two-order-parameter model of liquid that regards the liquid-liquid transition as the cooperative formation of locally favored structures. Thus, phase field calculations may allow us to predict the kinetics of liquid-liquid transitions and the resulting spatiotemporal change of various physical properties of the liquid, such as density and refractive index.

Spinodal of supercooled polarizable water

We develop a series of molecular dynamics computer simulations of liquid water, performed with a polarizable potential model, to calculate the spinodal line and the curve of maximum density inside the metastable supercooled region. After analyzing the structural properties, the liquid spinodal line is followed down to T=210K . A monotonic decrease is found in the explored region. The curve of maximum density bends on approaching the spinodal line. These results, in agreement with similar studies on nonpolarizable models of water, are consistent with the existence of a second critical point for water.

Effect of water-wall interaction potential on the properties of nanoconfined water

Much of the understanding of bulk liquids has progressed through study of the limiting case in which molecules interact via purely repulsive forces, such as a hard-core or "repulsive ramp" potential. In the same spirit, we report progress on the understanding of confined water by examining the behavior of waterlike molecules interacting with planar walls via purely repulsive forces and compare our results with those obtained for Lennard-Jones (LJ) interactions between the molecules and the walls. Specifically, we perform molecular dynamics simulations of 512 waterlike molecules interacting via the TIP5P potential and confined between two smooth planar walls that are separated by 1.1nm . At this separation, there are either two or three molecular layers of water, depending on density. We study two different forms of repulsive confinement, when the water-wall interaction potential is either (i) 1r;{9} or (ii) a WCA-like repulsive potential. We find that the thermodynamic, dynamic, and structural properties of the liquid in purely repulsive confinements qualitatively match those for a system with a pure LJ attraction to the wall. In previous studies that include attractions, freezing into monolayer or trilayer ice was seen for this wall separation. Using the same separation as these previous studies, we find that the crystal state is not stable with 1r;{9} repulsive walls but is stable with WCA-like repulsive confinement. However, by carefully adjusting the separation of the plates with 1r;{9} repulsive interactions so that the effective space available to the molecules is the same as that for LJ confinement, we find that the same crystal phases are stable. This result emphasizes the importance of comparing systems only using the same effective confinement, which may differ from the geometric separation of the confining surfaces.

Glass transition in biomolecules and the liquid-liquid critical point of water

Using molecular dynamics simulations, we investigate the relation between the dynamic transitions of biomolecules (lysozyme and DNA) and the dynamic and thermodynamic properties of hydration water. We find that the dynamic transition of the macromolecules, sometimes called a "protein glass transition," occurs at the temperature of dynamic crossover in the diffusivity of hydration water and also coincides with the maxima of the isobaric specific heat C_{P} and the temperature derivative of the orientational order parameter. We relate these findings to the hypothesis of a liquid-liquid critical point in water. Our simulations are consistent with the possibility that the protein glass transition results from crossing the Widom line, which is defined as the locus of correlation length maxima emanating from the hypothesized second critical point of water.

Four phases of amorphous water: Simulations versus experiment

Multiplicity of the liquid-liquid phase transitions in supercooled water, first obtained in computer simulations [Brovchenko et al., J. Chem. Phys. 118, 9473 (2003)], has got strong support from the recent experimental observation of the two phase transitions between amorphous ices [Loerting et al., Phys. Rev. Lett. 96, 025702 (2006)]. These experimental results allow assignment of the four amorphous water phases (I-IV) obtained in simulations to the three kinds of amorphous ices. Water phase I (rho approximately 0.90 gcm(3)) corresponds to the low-density amorphous ice, phase III (rho approximately 1.10 gcm(3)) to the high-density amorphous ice, and phase IV (rho approximately 1.20 gcm(3)) to the very-high-density amorphous ice. Phase II of model water with density rho approximately 1.00 gcm(3) corresponds to the normal-density water. Such assignment is confirmed by the comparison of the structural functions of the amorphous phases of model water and real water. In phases I and II the first and second coordination shells are clearly divided. Phase I consists mainly of the four coordinated tetrahedrally ordered water molecules. Phase II is enriched with molecules, which have tetrahedrally ordered four nearest neighbors and up six molecules in the first coordination shell. Majority of the molecules in phase III still have tetrahedrally ordered four nearest neighbors. Transition from phase III to phase IV is characterized by a noticeable drop of tetrahedral order, and phase IV consists mainly of molecules with highly isotropic angular distribution of the nearest neighbors. Relation between the structures of amorphous water phases, crystalline ices, and liquid water is discussed.

The melting point of ice Ih for common water models calculated from direct coexistence of the solid-liquid interface

In this work we present an implementation for the calculation of the melting point of ice I(h) from direct coexistence of the solid-liquid interface. We use molecular dynamics simulations of boxes containing liquid water and ice in contact. The implementation is based on the analysis of the evolution of the total energy along NpT simulations at different temperatures. We report the calculation of the melting point of ice I(h) at 1 bar for seven water models: SPC/E, TIP4P, TIP4P-Ew, TIP4P/ice, TIP4P/2005, TIP5P, and TIP5P-E. The results for the melting temperature from the direct coexistence simulations of this work are in agreement (within the statistical uncertainty) with those obtained previously by us from free energy calculations. By taking into account the results of this work and those of our free energy calculations, recommended values of the melting point of ice I(h) at 1 bar for the above mentioned water models are provided.

The relation between high-density and very-high-density amorphous ice

The exact nature of the relationship between high-density (HDA) and very-high-density (VHDA) amorphous ice is unknown at present. Here we review the relation between HDA and VHDA, concentrating on experimental aspects and discuss these with respect to the relation between low-density amorphous ice (LDA) and HDA. On compressing LDA at 125 K up to 1.5 GPa, two distinct density steps are observable in the pressure-density curves which correspond to the LDA --> HDA and HDA --> VHDA conversion. This stepwise formation process LDA --> HDA --> VHDA at 125 K is the first unambiguous observation of a stepwise amorphous-amorphous-amorphous transformation sequence. Density values of amorphous ice obtained in situ between 0.3 and 1.9 GPa on isobaric heating up to the temperatures of crystallization show a pronounced change of slope at ca. 0.8 GPa which could indicate formation of a distinct phase. We infer that the relation between HDA and VHDA is very similar to that between LDA and HDA except for a higher activation barrier between the former. We further discuss the two options of thermodynamic phase transition versus kinetic densification for the HDA --> VHDA conversion.

Family of tunable spherically symmetric potentials that span the range from hard spheres to waterlike behavior

We investigate the equation of state, diffusion coefficient, and structural order of a family of spherically symmetric potentials consisting of a hard core and a linear repulsive ramp. This generic potential has two characteristic length scales: the hard and soft core diameters. The family of potentials is generated by varying their ratio, lambda. We find negative thermal expansion (thermodynamic anomaly) and an increase of the diffusion coefficient upon isothermal compression (dynamic anomaly) for 0< or =lambda<6/7. As in water, the regions where these anomalies occur are nested domes in the (T, p) or (T, P) planes , with the thermodynamic anomaly dome contained entirely within the dynamic anomaly dome. We calculate translational and orientational order parameters (t and Q6), and project equilibrium state points onto the (t, Q6) plane, or order map. The order map evolves from waterlike behavior to hard-sphere-like behavior upon varying lambda between 4/7 and 6/7. Thus, we traverse the range of liquid behavior encompassed by hard spheres (lanbda=1) and waterlike (lambda approximately 4/7) with a family of tunable spherically symmetric potentials by simply varying the ratio of hard to soft-core diameters. Although dynamic and thermodynamic anomalies occur almost across the entire range 0< or=lambda< or=1, waterlike structural anomalies (i.e., decrease in both t and Q6 upon compression and strictly correlated T and Q6 in the anomalous region) occur only around lambda=4/7. Waterlike anomalies in structure, dynamics and thermodynamics arise solely due to the existence of two length scales, with their ratio lambda being the single control parameter, orientation-dependent interactions being absent by design.