Equilibrated High-Density Amorphous Ice and Its First-Order Transition to the Low-Density Form

Cooperative and Local Molecular Motion of High-Density Water in Glycerol Aqueous Solutions

The glass-to-liquid transition of water, particularly in high-density water (HDW), has long been a controversial topic due to challenges posed by inevitable crystallization. In this study, we addressed this issue by creating homogeneous high-density glass from a dilute glycerol aqueous solution under high pressure. Using dielectric spectroscopy, we explored the glass transition of HDW in glycerol solutions across the full concentration range under high pressures. HDW was found to exhibit two distinct relaxation modes: one linked to cooperative motion and the other to noncooperative local motion. The fragility index classification of HDW, derived from the cooperative motion of water, suggests that HDW behaves as a "fragile" liquid, contradicting previous suggestions. Extrapolation to pure HDW indicates that the dielectric relaxation observed in pure HDW originates from noncooperative local water motion.

Phase behavior of metastable water from large-scale simulations of a quantitatively accurate model near ambient conditions: The liquid-liquid critical point

The molecular mechanisms of water's unique anomalies are still debated upon. Experimental challenges have led to simulations suggesting a liquid-liquid (LL) phase transition, culminating in the supercooled region's LL critical point (LLCP). Computational expense, small system sizes, and the reliability of water models often limit these simulations. We adopt the CVF model, which is reliable, transferable, scalable, and efficient across a wide range of temperatures and pressures around ambient conditions. By leveraging the timescale separation between fast hydrogen bonds and slow molecular coordinates, the model allows a thorough exploration of the metastable phase diagram of liquid water. Using advanced numerical techniques to bypass dynamical slowing down, we perform finite-size scaling on larger systems than those used in previous analyses. Our study extrapolates thermodynamic behavior in the infinite-system limit, demonstrating the existence of the LLCP in the 3D Ising universality class in the low-temperature, low-pressure side of the line of temperatures of maximum density, specifically at TC = 186 ± 4 K and PC = 174 ± 14 MPa, at the end of a liquid-liquid phase separation stretching up to ∼200 MPa. These predictions align with recent experimental data and sophisticated models, highlighting that hydrogen bond cooperativity governs the LLCP and the origin of water anomalies. We also observe substantial cooperative fluctuations in the hydrogen bond network at scales larger than 10 nm, even at temperatures relevant to biopreservation. These findings have significant implications for nanotechnology and biophysics, providing new insights into water's behavior under varied conditions.

Unveiling a common phase transition pathway of high-density amorphous ices through time-resolved x-ray scattering

Here, we investigate the hypothesis that despite the existence of at least two high-density amorphous ices, only one high-density liquid state exists in water. We prepared a very-high-density amorphous ice (VHDA) sample and rapidly increased its temperature to around 205 ± 10 K using laser-induced isochoric heating. This temperature falls within the so-called "no-man's land" well above the glass-liquid transition, wherein the IR laser pulse creates a metastable liquid state. Subsequently, this high-density liquid (HDL) state of water decompresses over time, and we examined the time-dependent structural changes using short x-ray pulses from a free electron laser. We observed a liquid-liquid transition to low-density liquid water (LDL) over time scales ranging from 20 ns to 3 μs, consistent with previous experimental results using expanded high-density amorphous ice (eHDA) as the initial state. In addition, the resulting LDL derived both from VHDA and eHDA displays similar density and degree of inhomogeneity. Our observation supports the idea that regardless of the initial annealing states of the high-density amorphous ices, the same HDL and final LDL states are reached at temperatures around 205 K.

Tuning the low-temperature phase behavior of aqueous ionic liquids

Water's anomalous behavior is often explained using a two-liquid model, where two types of water, high-density liquid (HDL) and low-density liquid (LDL), can be separated via a liquid-liquid phase transition (LLPT) at low temperature. Mixtures of water and the ionic liquid hydrazinium trifluoroacetate were suggested to also show an LLPT but with the advantage that there is no rapid ice crystallization hampering its observation. It remains controversial whether these solutions exhibit an LLPT or are instead associated with complex phase separation phenomena. We here show detailed low-temperature calorimetry and diffraction experiments on aqueous solutions containing hydrazinium trifluoroacetate and other similar ionic liquids, all at a solute mole fraction of x = 0.175. Hydrazinium trifluoroacetate, ammonium trifluoroacetate, ethylammonium trifluoroacetate and hydrazinium pentafluoropropionate all boast exothermic transitions unrelated to crystallization as well as remarkable structural changes upon cooling into the glassy state. We propose a model inspired by micelle formation and decomposition in surfactant solutions, which is complemented by MD simulations and allows rationalizing the rich phase behavior of our mixtures during cooling. The fundamental aspect of the model is the hydrophobic nature of fluorinated anions that enables aggregation, which is reversed upon cooling and culminates in the remarkable exothermic first-order transition observed at low temperature. That is, we assign the first-order transition not to an LLPT but to phase-separations similar to the ones when falling below the Krafft temperature. All other solutions merely show simple vitrification behavior. Still, they exhibit distinct differences in liquid fragility, which is decreased continuously with decreasing hydrophobicity of the anions. This might enable the systematic tuning of ionic liquids with the goal of designing aqueous solutions of specific fragility.

Identification of local structures in water from supercooled to ambient conditions

Studies of water thermodynamics have long been tied to the identification of two distinct families of local structures, whose competition could explain the origin of the many thermodynamic anomalies and the hypothesized liquid-liquid critical point in water. Despite the many successes and insights gained, the structural indicators proposed throughout the years were not able to unequivocally identify these two families over a wide range of conditions. We show that a recently introduced indicator, Ψ, which exploits information on the hydrogen bond network connectivity, can reliably identify these two distinct local environments over a wide range of thermodynamic conditions (188-300 K and 0-13 kbar) and that close to the liquid-liquid critical point, the spatial correlations of density fluctuations are identical to those of the Ψ indicator. Our results strongly support the idea that water thermodynamic properties arise from the competition between two distinct and identifiable local environments.

A continuum of amorphous ices between low-density and high-density amorphous ice

Amorphous ices are usually classified as belonging to low-density or high-density amorphous ice (LDA and HDA) with densities ρLDA ≈ 0.94 g/cm3 and ρHDA ≈ 1.15-1.17 g/cm3. However, a recent experiment crushing hexagonal ice (ball-milling) produced a medium-density amorphous ice (MDA, ρMDA ≈ 1.06 g/cm3) adding complexity to our understanding of amorphous ice and the phase diagram of supercooled water. Motivated by the discovery of MDA, we perform computer simulations where amorphous ices are produced by isobaric cooling and isothermal compression/decompression. Our results show that, depending on the pressure employed, isobaric cooling can generate a continuum of amorphous ices with densities that expand in between those of LDA and HDA (briefly, intermediate amorphous ices, IA). In particular, the IA generated at P ≈ 125 MPa has a remarkably similar density and average structure as MDA, implying that MDA is not unique. Using the potential energy landscape formalism, we provide an intuitive qualitative understanding of the nature of LDA, HDA, and the IA generated at different pressures. In this view, LDA and HDA occupy specific and well-separated regions of the PEL; the IA prepared at P = 125 MPa is located in the intermediate region of the PEL that separates LDA and HDA.

Intrinsic Dynamics of Amorphous Ice Revealed by a Heterodyne Signal in X-ray Photon Correlation Spectroscopy Experiments

Unraveling the mechanism of water's glass transition and the interconnection between amorphous ices and liquid water plays an important role in our overall understanding of water. X-ray photon correlation spectroscopy (XPCS) experiments were conducted to study the dynamics and the complex interplay between the hypothesized glass transition in high-density amorphous ice (HDA) and the subsequent transition to low-density amorphous ice (LDA). Our XPCS experiments demonstrate that a heterodyne signal appears in the correlation function. Such a signal is known to originate from the interplay of a static component and a dynamic component. Quantitative analysis was performed on this heterodyne signal to extract the intrinsic dynamics of amorphous ice during the HDA-LDA transition. An angular dependence indicates non-isotropic, heterogeneous dynamics in the sample. Using the Stokes-Einstein relation to extract diffusion coefficients, the data are consistent with the scenario of static LDA islands floating within a diffusive matrix of high-density liquid water.

Supercooled solutions of sodium perchlorate in TIP4P/2005 water: The effect of martian solutes on thermodynamics and structure

We study the thermodynamic behavior of sodium perchlorate solutions in supercooled water through molecular dynamics numerical simulations. These solutions are of special interest because of the recent experimental results that led to hypothesize the presence of liquid water in perchlorate solutions beneath the Martian soil. We model water using the TIP4P/2005 potential. The results we obtain for solutions with concentrations 1.63 and 15.4 wt% are in agreement with those of a system undergoing a liquid-liquid phase transition where the liquid-liquid critical point shifts to slightly higher temperatures and lower pressures. The structure of the system is also analyzed, and we come to the conclusion that, even at the highest concentration considered, water retains its anomalous behavior.

Phase Diagram of Aqueous Solutions of LiCl: a Study of Concentration Effects on the Anomalies of Water

We perform molecular dynamics simulations in order to study thermodynamics and the structure of supercooled aqueous solutions of lithium chloride (LiCl) at concentrations c = 0.678 and 2.034 mol/kg. We model the solvent using the TIP4P/2005 potential and the ions using the Madrid-2019 force field, a force field particularly suited for studying this solution. We find that, for c = 0.678 mol/kg, the behavior of the equation of state, studied in the P-T plane, indicates the presence of a liquid-liquid phase transition, similar to what was previously found for bulk water. We estimate the position of the liquid-liquid critical point to be at T_c ≈ 174 K, P_c ≈ 1775 bar, and ρ_c ≈ 1.065 g/cm³. When the concentration is tripled to c = 2.034 mol/kg, no critical point is observed, indicating its possible disappearance at this concentration. We also study the water-water and water-ions structure in the two solutions, and we find that at the concentrations examined the effect of ions on the water-water structure is not strong, and all the features found in bulk water are preserved. We also calculate the hydration number of the Li and Cl ions, and in line with experiments, we find the value of 4 for Li⁺ and between 5.5 and 6 for Cl^-, confirming the good performances of the Madrid-2019 force field.

Nucleation and growth of crystalline ices from amorphous ices

We here review mostly experimental and some computational work devoted to nucleation in amorphous ices. In fact, there are only a handful of studies in which nucleation and growth in amorphous ices are investigated as two separate processes. In most studies, crystallization temperatures T_x or crystallization rates R_JG are accessed for the combined process. Our Review deals with different amorphous ices, namely, vapor-deposited amorphous solid water (ASW) encountered in many astrophysical environments; hyperquenched glassy water (HGW) produced from μm-droplets of liquid water; and low density amorphous (LDA), high density amorphous (HDA), and very high density amorphous (VHDA) ices produced via pressure-induced amorphization of ice I or from high-pressure polymorphs. We cover the pressure range of up to about 6 GPa and the temperature range of up to 270 K, where only the presence of salts allows for the observation of amorphous ices at such high temperatures. In the case of ASW, its microporosity and very high internal surface to volume ratio are the key factors determining its crystallization kinetics. For HGW, the role of interfaces between individual glassy droplets is crucial but mostly neglected in nucleation or crystallization studies. In the case of LDA, HDA, and VHDA, parallel crystallization kinetics to different ice phases is observed, where the fraction of crystallized ices is controlled by the heating rate. A key aspect here is that in different experiments, amorphous ices of different "purities" are obtained, where "purity" here means the "absence of crystalline nuclei." For this reason, "preseeded amorphous ice" and "nuclei-free amorphous ice" should be distinguished carefully, which has not been done properly in most studies. This makes a direct comparison of results obtained in different laboratories very hard, and even results obtained in the same laboratory are affected by very small changes in the preparation protocol. In terms of mechanism, the results are consistent with amorphous ices turning into an ultraviscous, deeply supercooled liquid prior to nucleation. However, especially in preseeded amorphous ices, crystallization from the preexisting nuclei takes place simultaneously. To separate the time scales of crystallization from the time scale of structure relaxation cleanly, the goal needs to be to produce amorphous ices free from crystalline ice nuclei. Such ices have only been produced in very few studies.

Amorphous NiFe Oxide-based Nanoreactors for Efficient Electrocatalytic Water Oxidation

Synergy engineering is an important way to enhance the kinetic activity of oxygen-evolution-reaction (OER) electrocatalysts. Here, we fabricated NiFe amorphous nanoreactor (NiFe-ANR) oxide as OER electrocatalysts via a mild self-catalytic reaction. Firstly, the amorphousness helps transform NiFe-ANR into highly active hydroxyhydroxides, and its many fine-grain boundaries increase active sites. More importantly, as proved by experiments and finite element analysis, the nanoreactor structure alters the spatial curvature and the mass transfer over the catalyst, thereby enriching OH^- in the catalyst surface and inner part. Thus, the catalyst with the structure of amorphous nanoreactors gained excellent activity, far superior to the NiFe catalyst with the structure of crystalline nanoreactor or amorphous non-nanoreactor. This work provides new insights into the applications and mechanisms of amorphousness and nanoreactors, embodying the "1+1>2" synergy of crystalline state and morphology.

Using coherent X-rays to follow dynamics in amorphous ices

Amorphous solid water plays an important role in our overall understanding of water's phase diagram. X-ray scattering is an important tool for characterising the different states of water, and modern storage ring and XFEL facilities have opened up new pathways to simultaneously study structure and dynamics. Here, X-ray photon correlation spectroscopy (XPCS) was used to study the dynamics of high-density amorphous (HDA) ice upon heating. We follow the structural transition from HDA to low-density amorphous (LDA) ice, by using wide-angle X-ray scattering (WAXS), for different heating rates. We used a new type of sample preparation, which allowed us to study μm-sized ice layers rather than powdered bulk samples. The study focuses on the non-equilibrium dynamics during fast heating, spontaneous transformation and crystallization. Performing the XPCS study at ultra-small angle (USAXS) geometry allows us to characterize the transition dynamics at length scales ranging from 60 nm-800 nm. For the HDA-LDA transition we observe a clear separation in three dynamical regimes, which show different dynamical crossovers at different length scales. The crystallization from LDA, instead, is observed to appear homogenously throughout the studied length scales.

Infrared Spectroscopy on Equilibrated High-Density Amorphous Ice

High-density (HDA) and low-density amorphous ices (LDA) are believed to be counterparts of the high- and low-density liquid phases of water, respectively. In order to better understand how the vibrational modes change during the transition between the two solid states, we present infrared spectroscopy measurements, following the change of the decoupled OD-stretch (vOD) (∼2460 cm-1) and OH-combinational mode (vOH + v2, vOH + 2vR) (∼5000 cm-1). We observe a redshift from HDA to LDA, accompanied with a drastic decrease of the bandwidth. The hydrogen bonds are stronger in LDA, which is caused by a change in the coordination number and number of water molecules interstitial between the first and second hydration shell. The unusually broad uncoupled OD band also clearly distinguishes HDA from other crystalline high-pressure phases, while the shape and position of the in situ prepared LDA are comparable to those of vapor-deposited amorphous ice.

Following the Crystallization of Amorphous Ice after Ultrafast Laser Heating

Using time-resolved wide-angle X-ray scattering, we investigated the early stages (10 μs–1 ms) of crystallization of supercooled water, obtained by the ultrafast heating of high- and low-density amorphous ice (HDA and LDA) up to a temperature T = 205 K ± 10 K. We have determined that the crystallizing phase is stacking disordered ice (I_sd), with a maximum cubicity of χ = 0.6, in agreement with predictions from molecular dynamics simulations at similar temperatures. However, we note that a growing small portion of hexagonal ice (I_h) was also observed, suggesting that within our timeframe, I_sd starts annealing into I_h. The onset of crystallization, in both amorphous ice, occurs at a similar temperature, but the observed final crystalline fraction in the LDA sample is considerably lower than that in the HDA sample. We attribute this discrepancy to the thickness difference between the two samples.

Oxygen NMR of high-density and low-density amorphous ice

Using oxygen-17 as a nuclear probe, spin relaxometry was applied to study the high-density and low-density states of amorphous ice, covering temperatures below and somewhat above their glass transitions. These findings are put in perspective with results from deuteron nuclear magnetic resonance and with calculations based on dielectrically detected correlation times. This comparison reveals the presence of a wide distribution of correlation times. Furthermore, oxygen-17 central-transition echo spectra were recorded for wide ranges of temperature and pulse spacing. The spectra cannot be described by a single set of quadrupolar parameters, suggesting a distribution of H–O–H opening angles that is broader for high-density than for low-density amorphous ice. Simulations of the pulse separation dependent spin-echo spectra for various scenarios demonstrate that a small-step frequency diffusion process, assigned to the presence of homonuclear oxygen–oxygen interactions, determines the shape evolution of the pulse-separation-dependent spectra.

The impact of temperature and unwanted impurities on slow compression of ice

For slowly compressed hexagonal ice pressure-induced amorphisation to high-density amorphous ice (HDA) takes place below and at 130 K, but polymorphic transformation to ice IX takes place at 140–170 K. Stable ice II only forms above 170 K. Ice IX impurities trigger ice IX growth even at 120 K. HDA and ice IX are equally long-lived, where both can be regarded as metastable phases.

Slow compression of ice at 100 K usually results in pressure-amorphisation, unless there are ice IX seeds and temperature gradients.

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.

The role of high-density and low-density amorphous ice on biomolecules at cryogenic temperatures: a case study with polyalanine

Experimental techniques, such as cryo-electron microscopy, require biological samples to be recovered at cryogenic temperatures (T ≈ 100 K) with water being in an amorphous ice state. However, (bulk) water can exist in two amorphous ices at P < 1 GPa, low-density amorphous (LDA) ice at low pressures and high-density amorphous ice (HDA) at high pressures; HDA is ≈20-25% denser than LDA. While fast/plunge cooling at 1 bar brings the sample into LDA, high-pressure cooling (HPC), at sufficiently high pressure, produces HDA. HDA can also be produced by isothermal compression of LDA at cryogenic temperatures. Here, we perform classical molecular dynamics simulations to study the effects of LDA, HDA, and the LDA-HDA transformation on the structure and hydration of a small peptide, polyalanine. We follow thermodynamic paths corresponding to (i) fast/plunge cooling at 1 bar, (ii) HPC at P = 400 MPa, and (iii) compression/decompression cycles at T = 80 K. While process (i) produced LDA in the system, path (iii) produces HDA. Interestingly, the amorphous ice produced in process (ii) is an intermediate amorphous ice (IA) with properties that fall in-between those of LDA and HDA. Remarkably, the structural changes in polyalanine are negligible at all conditions studied (0-2000 MPa, 80-300 K) even when water changes among the low and high-density liquid states as well as the amorphous solids LDA, IA, and HDA. The similarities and differences in the hydration of polyalanine vitrified in LDA, IA, and HDA are described. Since the studied thermodynamic paths are suitable for the cryopreservation of biomolecules, we also study the structure and hydration of polyalanine along isobaric and isochoric heating paths, which can be followed experimentally for the recovery of cryopreserved samples. Upon heating, the structure of polyalanine remains practically unchanged. We conclude with a brief discussion of the practical advantages of (a) using HDA and IA as a cryoprotectant environment (as opposed to LDA), and (b) the use of isochoric heating as a recovery process (as opposed to isobaric heating).

Structural investigation of three distinct amorphous forms of Ar hydrate

Three amorphous forms of Ar hydrate were produced using the crystalline clathrate hydrate Ar·6.5H₂O (structure II, Fd3̄m, a ≈ 17.1 Å) as a precursor and structurally characterized by a combination of isotope substitution (³⁶Ar) neutron diffraction and molecular dynamics (MD) simulations. The first form followed from the pressure-induced amorphization of the precursor at 1.5 GPa at 95 K and the second from isobaric annealing at 2 GPa and subsequent cooling back to 95 K. In analogy to amorphous ice, these amorphs are termed high-density amorphous (HDA) and very-high-density amorphous (VHDA), respectively. The third amorph (recovered amorphous, RA) was obtained when recovering VHDA to ambient pressure (at 95 K). The three amorphs have distinctly different structures. In HDA the distinction of the original two crystallographically different Ar guests is maintained as differently dense Ar–water hydration structures, which expresses itself in a split first diffraction peak in the neutron structure factor function. Relaxation of the local water structure during annealing produces a homogeneous hydration environment around Ar, which is accompanied with a densification by about 3%. Upon pressure release the homogeneous amorphous structure undergoes expansion by about 21%. Both VHDA and RA can be considered frozen solutions of immiscible Ar and water in which in average 15 and 11 water molecules, respectively, coordinate Ar out to 4 Å. The local water structures of HDA and VHDA Ar hydrates show some analogy to those of the corresponding amorphous ices, featuring H₂O molecules in 5- and 6-fold coordination with neighboring molecules. However, they are considerably less dense. Most similarity is seen between RA and low density amorphous ice (LDA), which both feature strictly 4-coordinated H₂O networks. It is inferred that, depending on the kind of clathrate structure and occupancy of cages, amorphous states produced from clathrate hydrates display variable local water structures.

Three amorphous forms of Ar clathrate hydrate (pressure-amorphized, annealed and recovered) were characterized by isotope substitution (³⁶Ar) neutron diffraction and molecular dynamics and their local coordinations analyzed and compared to pure ice.

Experimental evidence for glass polymorphism in vitrified water droplets

The question of whether a first-order liquid-to-liquid transition is at the origin of water’s anomalous properties has been controversial since the pioneering experiments by Mishima et al. in 1985 and molecular simulations by Poole et al. in 1992. Since then, experiments aimed at shedding light on this question have been performed using amorphous ices made from crystalline ice, fueling criticism about their crystal-like nature. In the present study, we avoid crystalline ice at any time of the experiment yet still observe a first-order glass-to-glass transition in vitrified liquid droplets. This makes the strong case for glass polymorphism and the direct thermodynamic connection to the liquid-to-liquid transition at higher temperatures, dismissing the criticism voiced for three decades.

The nature of amorphous ices has been debated for more than 35 years. In essence, the question is whether they are related to ice polymorphs or to liquids. The fact that amorphous ices are traditionally prepared from crystalline ice via pressure-induced amorphization has made a clear distinction tricky. In this work, we vitrify liquid droplets through cooling at ≥10⁶ K ⋅ s⁻¹ and pressurize the glassy deposit. We observe a first order–like densification upon pressurization and recover a high-density glass. The two glasses resemble low- and high-density amorphous ice in terms of both structure and thermal properties. Vitrified water shows all features that have been reported for amorphous ices made from crystalline ice. The only difference is that the hyperquenched and pressurized deposit shows slightly different crystallization kinetics to ice I upon heating at ambient pressure. This implies a thermodynamically continuous connection of amorphous ices with liquids, not crystals.

Experimental observation of the liquid-liquid transition in bulk supercooled water under pressure

We prepared bulk samples of supercooled liquid water under pressure by isochoric heating of high-density amorphous ice to temperatures of 205 ± 10 kelvin, using an infrared femtosecond laser. Because the sample density is preserved during the ultrafast heating, we could estimate an initial internal pressure of 2.5 to 3.5 kilobar in the high-density liquid phase. After heating, the sample expanded rapidly, and we captured the resulting decompression process with femtosecond x-ray laser pulses at different pump-probe delay times. A discontinuous structural change occurred in which low-density liquid domains appeared and grew on time scales between 20 nanoseconds to 3 microseconds, whereas crystallization occurs on time scales of 3 to 50 microseconds. The dynamics of the two processes being separated by more than one order of magnitude provides support for a liquid-liquid transition in bulk supercooled water.

Electron Beam-Induced Transformation in High-Density Amorphous Ices

Amorphous ice is commonly used as a noncrystalline matrix for protecting sensitive biological samples in cryogenic electron microscopy (cryo-EM). The amorphization process of water is complex, and at least two amorphous states of different densities are known to exist, high- and low-density amorphous ices (HDA and LDA). These forms are considered to be the counterparts of two distinct liquid states, namely, high- and low-density liquid water. Herein, we investigate the HDA to LDA transition using electron diffraction and cryo-EM. The observed phase transition is induced by the impact of electrons, and we discuss two different mechanisms, namely, local heating and beam-induced motion of water molecules. The temperature increase is estimated by comparison with X-ray scattering experiments on identically prepared samples. Our results suggest that HDA, under the conditions used in our cryo-EM measurements, is locally heated above its glass-transition temperature.

The anomalies and criticality of liquid water

The origin of water's anomalies has been a matter of long-standing debate. A two-state model, dating back to Röntgen, relies on the dynamical coexistence of two types of local structures-locally favored tetrahedral structure (LFTS) and disordered normal-liquid structure (DNLS)-in liquid water. Phenomenologically, this model not only explains water's thermodynamic anomalies but also can rationalize the existence of a liquid-liquid critical point (LLCP) if there is a cooperative formation of LFTS. We recently found direct evidence for the coexistence of LFTS and DNLS in the experimental structure factor of liquid water. However, the existence of the LLCP and its impact on water's properties has remained elusive, leaving the origin of water's anomalies unclear. Here we propose a unique strategy to locate the LLCP of liquid water. First, we make a comprehensive analysis of a large set of experimental structural, thermodynamic, and dynamic data based on our hierarchical two-state model. This model predicts that the two thermodynamic and dynamical fluctuation maxima lines should cross at the LLCP if it exists, which we confirm by hundred-microsecond simulations for model waters. Based on recent experimental results of the compressibility and diffusivity measurements in the no man's land, we reveal that the two lines cross around 184 K and 173 MPa for real water, suggesting the presence of the LLCP around there. Nevertheless, we find that the criticality is almost negligible in the experimentally accessible region of liquid water because it is too far from the LLCP. Our findings would provide a clue to settle the long-standing debate.

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.

Structural differences between unannealed and expanded high-density amorphous ice based on isotope substitution neutron diffraction

We here report isotope substitution neutron diffraction experiments on two variants of high-density amorphous ice (HDA): its unannealed form prepared via pressure-induced amorphization of hexagonal ice at 77 K, and its expanded form prepared via decompression of very-high density amorphous ice at 140 K. The latter is about 17 K more stable thermally, so that it can be heated beyond its glass-to-liquid transition to the ultraviscous liquid form at ambient pressure. The structural origin for this large thermal difference and the possibility to reach the deeply supercooled liquid state has not yet been understood. Here we reveal that the origin for this difference is found in the intermediate range structure, beyond about 3.6 Å. The hydration shell markedly differs at about 6 Å. The local order, by contrast, including the first as well as the interstitial space between first and second shell is very similar for both. 'eHDA' that is decompressed to 0.20 GPa instead of 0.07 GPa is here revealed to be rather far away from well-relaxed eHDA. Instead it turns out to be roughly halfway between VHDA and eHDA - stressing the importance for decompressing VHDA to at least 0.10 GPa to make an eHDA sample of good quality.

X-ray studies of the transformation from high- to low-density amorphous water

Here we report about the structural evolution during the conversion from high-density amorphous ices at ambient pressure to the low-density state. Using high-energy X-ray diffraction, we have monitored the transformation by following in reciprocal space the structure factor S_OO( Q) and derived in real space the pair distribution function g_OO( r). Heating equilibrated high-density amorphous ice (eHDA) at a fast rate (4 K min^-1), the transition to the low-density form occurs very rapidly, while domains of both high- and low-density coexist. On the other hand, the transition in the case of unannealed HDA (uHDA) and very-high-density amorphous ice is more complex and of continuous nature. The direct comparison of eHDA and uHDA indicates that the molecular structure of uHDA contains a larger amount of tetrahedral motives. The different crystallization behaviour of the derived low-density amorphous states is interpreted as emanating from increased tetrahedral coordination present in uHDA. This article is part of the theme issue 'The physics and chemistry of ice: scaffolding across scales, from the viability of life to the formation of planets'.

Evidence for high-density liquid water between 0.1 and 0.3 GPa near 150 K

Thermal stability against crystallization upon isobaric heating at pressure 0.1 ≤ P ≤ 1.9 GPa is compared for five variants of high- (HDA) and very high-density amorphous ice (VHDA) with different preparation history. At 0.1-0.3 GPa expanded HDA (eHDA) and VHDA reach the same state before crystallization, which we infer to be the contested high-density liquid (HDL). Thus, 0.3 GPa sets the high-pressure limit for the possibility to observe HDL for timescales of minutes, hours, and longer. At P > 0.3 GPa the annealed amorphous ices no longer reach the same state before crystallization. Further examination of the results demonstrates that crystallization times are significantly affected both by the density of the amorphous matrix at the crystallization temperature T _x as well as by nanocrystalline domains remaining in unannealed HDA (uHDA) as a consequence of incomplete pressure-induced amorphization.

Unravelling the contribution of local structures to the anomalies of water: The synergistic action of several factors

We investigate the microscopic origin of water's anomalies by inspecting the hydrogen bond network (HBN) and the spatial organization of low-density-liquid (LDL) like and high-density-liquid (HDL) like environments. Specifically, we simulate-via classical molecular dynamics simulations-the isobaric cooling of a sample composed of 512 water molecules from ambient to deeply undercooled conditions at three pressures, namely, 1 bar, 400 bars, and 1000 bars. In correspondence with the Widom line (WL), (i) the HDL-like dominating cluster undergoes fragmentation caused by the percolation of LDL-like aggregates following a spinodal-like kinetics; (ii) such fragmentation always occurs at a "critical" concentration of ∼20%-30% in LDL; (iii) the HBN within LDL-like environments is characterized by an equal number of pentagonal and hexagonal rings that create a state of maximal frustration between a configuration that promotes crystallization (hexagonal ring) and a configuration that hinders it (pentagonal ring); (iv) the spatial organization of HDL-like environments shows a marked variation. Moreover, the inspection of the global symmetry shows that the intermediate-range order decreases in correspondence with the WL and such a decrease becomes more pronounced upon increasing the pressure, hence supporting the hypothesis of a liquid-liquid critical point. Our results reveal and rationalize the complex microscopic origin of water's anomalies as the cooperative effect of several factors acting synergistically. Beyond implications for water, our findings may be extended to other materials displaying anomalous behaviours.

X-ray Scattering and O-O Pair-Distribution Functions of Amorphous Ices

The structure factor and oxygen–oxygen pair-distribution functions of amorphous ices at liquid nitrogen temperature (T = 77 K) have been derived from wide-angle X-ray scattering (WAXS) up to interatomic distances of r = 23 Å, where local structure differences between the amorphous ices can be seen for the entire range. The distances to the first coordination shell for low-, high-, and very-high-density amorphous ice (LDA, HDA, VHDA) were determined to be 2.75, 2.78, and 2.80 Å, respectively, with high accuracy due to measurements up to a large momentum transfer of 23 Å^–1. Similarities in pair-distribution functions between LDA and supercooled water at 254.1 K, HDA and liquid water at 365.9 K, and VHDA and high-pressure liquid water were found up to around 8 Å, but beyond that at longer distances, the similarities were lost. In addition, the structure of the high-density amorphous ices was compared to high-pressure crystalline ices IV, IX , and XII, and conclusions were drawn about the local ordering.

Heating- and pressure-induced transformations in amorphous and hexagonal ice: A computer simulation study using the TIP4P/2005 model

We characterize the phase behavior of glassy water by performing extensive out-of-equilibrium molecular dynamics simulations using the TIP4P/2005 water model. Specifically, we study (i) the pressure-induced transformations between low-density (LDA) and high-density amorphous ice (HDA), (ii) the pressure-induced amorphization (PIA) of hexagonal ice (I_h), (iii) the heating-induced LDA-to-HDA transformation at high pressures, (iv) the heating-induced HDA-to-LDA transformation at low and negative pressures, (v) the glass transition temperatures of LDA and HDA as a function of pressure, and (vi) the limit of stability of LDA upon isobaric heating and isothermal decompression (at negative pressures). These transformations are studied systematically, over a wide range of temperatures and pressures, allowing us to construct a P-T phase diagram for glassy TIP4P/2005 water. Our results are in qualitative agreement with experimental observations and with the P-T phase diagram obtained for glassy ST2 water that exhibits a liquid-liquid phase transition and critical point. We also discuss the mechanism for PIA of ice I_h and show that this is a two-step process where first, the hydrogen-bond network (HBN) is distorted and then the HBN abruptly collapses. Remarkably, the collapse of the HB in ice I_h occurs when the average molecular orientations order, a measure of the tetrahedrality of the HBN, is of the same order as in LDA, suggesting a common mechanism for the LDA-to-HDA and I_h-to-HDA transformations.

Relaxation dynamics and transformation kinetics of deeply supercooled water: Temperature, pressure, doping, and proton/deuteron isotope effects

Above its glass transition, the equilibrated high-density amorphous ice (HDA) transforms to the low-density pendant (LDA). The temperature dependence of the transformation is monitored at ambient pressure using dielectric spectroscopy and at elevated pressures using dilatometry. It is found that near the glass transition temperature of deuterated samples, the transformation kinetics is 300 times slower than the structural relaxation, while for protonated samples, the time scale separation is at least 30 000 and insensitive to doping. The kinetics of the HDA to LDA transformation lacks a proton/deuteron isotope effect, revealing that this process is dominated by the restructuring of the oxygen network. The x-ray diffraction experiments performed on samples at intermediate transition stages reflect a linear combination of the LDA and HDA patterns implying a macroscopic phase separation, instead of a local intermixing of the two amorphous states.

On the crystallisation temperature of very high-density amorphous ice

The influence of the protocol of preparation on the crystallisation temperature TX of very high-density amorphous ice (VHDA) was studied by varying the annealing pressure (1.1, 1.6 and 1.9 GPa) and temperature (160, 167 and 175 K, respectively). TX increases by up to 4 K in the pressure range of 0.7 to 1.8 GPa for samples annealed at 1.9 GPa compared to samples annealed at 1.1 GPa. Concomitantly, secondary crystallisation channels are suppressed, indicating the absence of structural inhomogeneities. For VHDA prepared at 1.1 GPa and 1.6 GPa our results indicate such inhomogeneities, which we regard to be incompletely amorphized, distorted nanodomains of hexagonal ice that cannot be detected through X-ray diffraction experiments. VHDA prepared at high pressures and temperatures thus represents the amorphous state of water at >0.7 GPa least affected by nanocrystals that has been described so far. We expect the TX obtained for the samples prepared in this manner to be close to the ultimate limit, i.e., we do not consider it possible to raise the low-temperature border to the no-man's land notably further by changing the preparation protocol. An additional, considerable increase in this border will only be possible by working at much shorter time-scales, e.g., by employing fast heating experiments.

Calorimetric study of water's two glass transitions in the presence of LiCl

A DSC study of dilute glassy LiCl aqueous solutions in the water-dominated regime provides direct evidence of a glass-to-liquid transition in expanded high density amorphous (eHDA)-type solutions. Similarly, low density amorphous ice (LDA) exhibits a glass transition prior to crystallization to ice Ic. Both glass transition temperatures are independent of the salt concentration, whereas the magnitude of the heat capacity increase differs. By contrast to pure water, the glass transition endpoint for LDA can be accessed in LiCl aqueous solutions above 0.01 mole fraction. Furthermore, we also reveal the endpoint for HDA's glass transition, solving the question on the width of both glass transitions. This suggests that both equilibrated HDL and LDL can be accessed in dilute LiCl solutions, supporting the liquid-liquid transition scenario to understand water's anomalies.

High-density amorphous ice: nucleation of nanosized low-density amorphous ice

The pressure dependence of the crystallization temperature of different forms of expanded high-density amorphous ice (eHDA) was scrutinized. Crystallization at pressures 0.05-0.30 GPa was followed using volumetry and powder x-ray diffraction. eHDA samples were prepared via isothermal decompression of very high-density amorphous ice at 140 K to different end pressures between 0.07-0.30 GPa (eHDA^0.07-0.3). At 0.05-0.17 GPa the crystallization line T _x (p) of all eHDA variants is the same. At pressures  >0.17 GPa, all eHDA samples decompressed to pressures  <0.20 GPa exhibit significantly lower T _x values than eHDA^0.2 and eHDA^0.3. We rationalize our findings with the presence of nanoscaled low-density amorphous ice (LDA) seeds that nucleate in eHDA when it is decompressed to pressures  <0.20 GPa at 140 K. Below ~0.17 GPa, these nanosized LDA domains are latent within the HDA matrix, exhibiting no effect on T _x of eHDA^<0.2. Upon heating at pressures  ⩾0.17 GPa, these nanosized LDA nuclei transform to ice IX nuclei. They are favored sites for crystallization and, hence, lower T _x . By comparing crystallization experiments of bulk LDA with the ones involving nanosized LDA we are able to estimate the Laplace pressure and radius of ~0.3-0.8 nm for the nanodomains of LDA. The nucleation of LDA in eHDA revealed here is evidence for the first-order-like nature of the HDA  →  LDA transition, supporting water's liquid-liquid transition scenarios.

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.

Large-Scale Structure and Hyperuniformity of Amorphous Ices

We investigate the large-scale structure of amorphous ices and transitions between their different forms by quantifying their large-scale density fluctuations. Specifically, we simulate the isothermal compression of low-density amorphous ice (LDA) and hexagonal ice to produce high-density amorphous ice (HDA). Both HDA and LDA are nearly hyperuniform; i.e., they are characterized by an anomalous suppression of large-scale density fluctuations. By contrast, in correspondence with the nonequilibrium phase transitions to HDA, the presence of structural heterogeneities strongly suppresses the hyperuniformity and the system becomes hyposurficial (devoid of "surface-area fluctuations"). Our investigation challenges the largely accepted "frozen-liquid" picture, which views glasses as structurally arrested liquids. Beyond implications for water, our findings enrich our understanding of pressure-induced structural transformations in glasses.

Diffusive dynamics during the high-to-low density transition in amorphous ice

Water exists in high- and low-density amorphous ice forms (HDA and LDA), which could correspond to the glassy states of high- (HDL) and low-density liquid (LDL) in the metastable part of the phase diagram. However, the nature of both the glass transition and the high-to-low-density transition are debated and new experimental evidence is needed. Here we combine wide-angle X-ray scattering (WAXS) with X-ray photon-correlation spectroscopy (XPCS) in the small-angle X-ray scattering (SAXS) geometry to probe both the structural and dynamical properties during the high-to-low-density transition in amorphous ice at 1 bar. By analyzing the structure factor and the radial distribution function, the coexistence of two structurally distinct domains is observed at T = 125 K. XPCS probes the dynamics in momentum space, which in the SAXS geometry reflects structural relaxation on the nanometer length scale. The dynamics of HDA are characterized by a slow component with a large time constant, arising from viscoelastic relaxation and stress release from nanometer-sized heterogeneities. Above 110 K a faster, strongly temperature-dependent component appears, with momentum transfer dependence pointing toward nanoscale diffusion. This dynamical component slows down after transition into the low-density form at 130 K, but remains diffusive. The diffusive character of both the high- and low-density forms is discussed among different interpretations and the results are most consistent with the hypothesis of a liquid-liquid transition in the ultraviscous regime.