Interplay of vitrification and ice formation in a cryoprotectant aqueous solution at low temperature.

The proneness of water to crystallize is a major obstacle to understanding its putative exotic behavior in the supercooled state. It also represents a strong practical limitation to cryopreservation of biological systems. Adding some concentration of glycerol, which has a cryoprotective effect preventing, to some degree, water crystallization, has been proposed as a possible way out, provided the concentration is small enough for water to retain some of its bulk character and/or for limiting the damage caused by glycerol on living organisms. Contrary to previous expectations, we show that, in the "marginal" glycerol molar concentration ≈ 18%, at which vitrification is possible with no crystallization on rapid cooling, water crystallizes upon isothermal annealing even below the calorimetric glass transition of the solution. Through a time-resolved polarized neutron scattering investigation, we extract key parameters, size and shape of the ice crystallites, fraction of water that crystallizes, and crystallization time, which are important for cryoprotection, as a function of the annealing temperature. We also characterize the nature of the out-of-equilibrium liquid phases that are present at low temperature, providing more arguments against the presence of an isocompositional liquid­liquid transition. Finally, we propose a rule of thumb to estimate the lower temperature limit below which water crystallization does not occur in aqueous solutions.

Crystal Nucleation in Supercooled Atomic Liquids.

The liquid-to-solid phase transition is a complex process that is difficult to investigate experimentally with sufficient spatial and temporal resolution. A key aspect of the transition is the formation of a critical seed of the crystalline phase in a supercooled liquid, that is, a liquid in a metastable state below the melting temperature. This stochastic process is commonly described within the framework of classical nucleation theory, but accurate tests of the theory in atomic and molecular liquids are challenging. Here, we employ femtosecond x-ray diffraction from microscopic liquid jets to study crystal nucleation in supercooled liquids of the rare gases argon and krypton. Our results provide stringent limits to the validity of classical nucleation theory in atomic liquids, and offer the long-sought possibility of testing nonclassical extensions of the theory.

Isotope effect on the anomalies of water: A corresponding states analysis.

Light and heavy water show similar anomalies in thermodynamic and dynamic properties, with a consistent trend of anomalies occurring at higher temperatures in heavy water. Viscosity also increases faster upon cooling in heavy water, causing a giant isotope effect, with a viscosity ratio near 2.4 at 244 K. While a simple temperature shift apparently helps in collapsing experimental data for both isotopes, it lacks a clear justification, changes value with the property considered, and requires additional ad hoc scaling factors. Here, we use a corresponding states analysis based on the possible existence of a liquid-liquid critical point in supercooled water. This provides a coherent framework that leads to the collapse of thermodynamic data. The ratio between the dynamic properties of the isotopes is strongly reduced. In particular, the decoupling between viscosity η and self-diffusion D, measured as a function of temperature T by the Stokes-Einstein ratio Dη/T, is found to collapse after applying the corresponding states analysis. Our results are consistent with simulations and suggest that the various isotope effects mirror the one on the liquid-liquid transition.

Viscosity and Stokes-Einstein relation in deeply supercooled water under pressure.

We report measurements of the shear viscosity η in water up to 150 MPa and down to 229.5 K. This corresponds to more than 30 K supercooling below the melting line. The temperature dependence is non-Arrhenius at all pressures, but its functional form at 0.1 MPa is qualitatively different from that at all pressures above 20 MPa. The pressure dependence is non-monotonic, with a pressure-induced decrease of viscosity by more than 50% at low temperature. Combining our data with literature data on the self-diffusion coefficient Ds of water, we check the Stokes-Einstein relation which, based on hydrodynamics, predicts constancy of Dsη/T, where T is the temperature. The observed temperature and pressure dependence of Dsη/T is analogous to that obtained in simulations of a realistic water model. This analogy suggests that our data are compatible with the existence of a liquid-liquid critical point at positive pressure in water.

Effects of compressibility and wetting on the liquid-vapor transition in a confined fluid.

When a fluid is constrained to a fixed, finite volume, the conditions for liquid-vapor equilibrium are different from those for the infinite volume or constant pressure cases. There is even a range of densities for which no bubble can form, and the liquid at a pressure below the bulk saturated vapor pressure remains indefinitely stable. As the fluid density in mineral inclusions is often derived from the temperature of bubble disappearance, a correction for the finite volume effect is required. Previous works have explained these phenomena and proposed a numerical procedure to compute the correction for pure water in a container completely wet by the liquid phase. Here, we revisit these works and provide an analytic formulation valid for any fluid, including the case of partial wetting. We introduce the Berthelot-Laplace length λ = 2γκ/3, which combines the liquid isothermal compressibility κ and its surface tension γ. The quantitative effects are fully captured by a single, nondimensional parameter: the ratio of λ to the container size.

Minimal Microscopic Model for Liquid Polyamorphism and Waterlike Anomalies.

Liquid polyamorphism is the intriguing possibility for a single component substance to exist in multiple liquid phases. We propose a minimal model for this phenomenon. Starting with a binary lattice model with critical azeotropy and liquid-liquid demixing, we allow interconversion of the two species, turning the system into a single-component fluid with two states differing in energy and entropy. Unveiling the phase diagram of the noninterconverting binary mixture gives unprecedented insight on the phase behaviors accessible to the interconverting fluid, such as a liquid-liquid transition with a critical point, or a singularity-free scenario, exhibiting thermodynamic anomalies without polyamorphism. The model provides a unified theoretical framework to describe supercooled water and a variety of polyamorphic liquids with waterlike anomalies.

High Pressure Inside Nanometer-Sized Particles Influences the Rate and Products of Chemical Reactions.

The composition of organic aerosol has a pivotal influence on aerosol properties such as toxicity and cloud droplet formation capability, which could affect both climate and air quality. However, a comprehensive and fundamental understanding of the chemical and physical processes that occur in nanometer-sized atmospheric particles remains a challenge that severely limits the quantification and predictive capabilities of aerosol formation pathways. Here, we investigated the effects of a fundamental and hitherto unconsidered physical property of nanoparticles-the Laplace pressure. By studying the reaction of glyoxal with ammonium sulfate, both ubiquitous and important atmospheric constituents, we show that high pressure can significantly affect the chemical processes that occur in atmospheric ultrafine particles (i.e., particles < 100 nm). Using high-resolution mass spectrometry and UV-vis spectroscopy, we demonstrated that the formation of reaction products is strongly (i.e., up to a factor of 2) slowed down under high pressures typical of atmospheric nanoparticles. A size-dependent relative rate constant is determined and numerical simulations illustrate the reduction in the production of the main glyoxal reaction products. These results established that the high pressure inside nanometer-sized aerosols must be considered as a key property that significantly impacts chemical processes that govern atmospheric aerosol growth and evolution.

Effect of dissolved salt on the anomalies of water at negative pressure.

Adding salt to water at ambient pressure affects its thermodynamic properties. At low salt concentration, anomalies such as the density maximum are shifted to lower temperature, while at large enough salt concentration, they cannot be observed any more. Here, we investigate the effect of salt on an anomaly recently observed in pure water at negative pressure: the existence of a sound velocity minimum along isochores. We compare experiments and simulations for an aqueous solution of sodium chloride with molality around 1.2 mol kg-1, reaching pressures beyond -100 MPa. We also discuss the origin of the minima in the sound velocity and emphasize the importance of the relative position of the temperatures of sound velocity and density anomalies.

Pressure dependence of viscosity in supercooled water and a unified approach for thermodynamic and dynamic anomalies of water.

The anomalous decrease of the viscosity of water with applied pressure has been known for over a century. It occurs concurrently with major structural changes: The second coordination shell around a molecule collapses onto the first shell. Viscosity is thus a macroscopic witness of the progressive breaking of the tetrahedral hydrogen bond network that makes water so peculiar. At low temperature, water at ambient pressure becomes more tetrahedral and the effect of pressure becomes stronger. However, surprisingly, no data are available for the viscosity of supercooled water under pressure, in which dramatic anomalies are expected based on interpolation between ambient pressure data for supercooled water and high pressure data for stable water. Here we report measurements with a time-of-flight viscometer down to [Formula: see text] and up to [Formula: see text], revealing a reduction of viscosity by pressure by as much as 42%. Inspired by a previous attempt [Tanaka H (2000) J Chem Phys 112:799-809], we show that a remarkably simple extension of a two-state model [Holten V, Sengers JV, Anisimov MA (2014) J Phys Chem Ref Data 43:043101], initially developed to reproduce thermodynamic properties, is able to accurately describe dynamic properties (viscosity, self-diffusion coefficient, and rotational correlation time) as well. Our results support the idea that water is a mixture of a high density, "fragile" liquid, and a low density, "strong" liquid, the varying proportion of which explains the anomalies and fragile-to-strong crossover in water.

Thermodynamics of supercooled and stretched water: Unifying two-structure description and liquid-vapor spinodal.

We have applied a two-structure approach to the description of the thermodynamic properties of supercooled and stretched water, metastable toward vapor, ice, or both, by incorporating the stability limit of liquid with respect to vapor at negative pressures. In addition to the properties of water considered in previous studies, we include new data recently obtained in deeply supercooled and stretched regions. Our model reproduces the experimentally observed anomalies in metastable water up to 400 MPa and down to -140 MPa, and can provide a physically based extrapolation in regions where no measurements are available yet. Moreover, we are able to elucidate the thermodynamic nature of the alternative "states" of liquid water, namely, high-temperature denser water (state A) and "mother-of-ice" lighter water (state B). Based on the internal consistency of the described anomalies and new data on the isothermal compressibility, we exclude the critical-point-free scenario in which the first-order liquid-liquid transition line would continue into the stretched liquid state (doubly metastable) crossing the vapor-liquid spinodal. A "singularity-free" scenario remains an option for explaining supercooled water's anomalies within the framework of two-state thermodynamics; however, the extreme case of the singularity-free scenario, ideal mixing of A and B, seems improbable. We have also clarified the concept of fast interconversion of alternative states in supercooled water as a phenomenological representation of distribution of short-ranged local structures.

Molecular mechanism for cavitation in water under tension.

Despite its relevance in biology and engineering, the molecular mechanism driving cavitation in water remains unknown. Using computer simulations, we investigate the structure and dynamics of vapor bubbles emerging from metastable water at negative pressures. We find that in the early stages of cavitation, bubbles are irregularly shaped and become more spherical as they grow. Nevertheless, the free energy of bubble formation can be perfectly reproduced in the framework of classical nucleation theory (CNT) if the curvature dependence of the surface tension is taken into account. Comparison of the observed bubble dynamics to the predictions of the macroscopic Rayleigh-Plesset (RP) equation, augmented with thermal fluctuations, demonstrates that the growth of nanoscale bubbles is governed by viscous forces. Combining the dynamical prefactor determined from the RP equation with CNT based on the Kramers formalism yields an analytical expression for the cavitation rate that reproduces the simulation results very well over a wide range of pressures. Furthermore, our theoretical predictions are in excellent agreement with cavitation rates obtained from inclusion experiments. This suggests that homogeneous nucleation is observed in inclusions, whereas only heterogeneous nucleation on impurities or defects occurs in other experiments.

Shrinking of Rapidly Evaporating Water Microdroplets Reveals their Extreme Supercooling.

The fast evaporative cooling of micrometer-sized water droplets in a vacuum offers the appealing possibility to investigate supercooled water-below the melting point but still a liquid-at temperatures far beyond the state of the art. However, it is challenging to obtain a reliable value of the droplet temperature under such extreme experimental conditions. Here, the observation of morphology-dependent resonances in the Raman scattering from a train of perfectly uniform water droplets allows us to measure the variation in droplet size resulting from evaporative mass losses with an absolute precision of better than 0.2%. This finding proves crucial to an unambiguous determination of the droplet temperature. In particular, we find that a fraction of water droplets with an initial diameter of 6379±12 nm remain liquid down to 230.6±0.6 K. Our results question temperature estimates reported recently for larger supercooled water droplets and provide valuable information on the hydrogen-bond network in liquid water in the hard-to-access deeply supercooled regime.

Erratum: Shrinking of Rapidly Evaporating Water Microdroplets Reveals their Extreme Supercooling [Phys. Rev. Lett. 120, 015501 (2018)].

This corrects the article DOI: 10.1103/PhysRevLett.120.015501.

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.

Viscosity and self-diffusion of supercooled and stretched water from molecular dynamics simulations.

Among the numerous anomalies of water, the acceleration of dynamics under pressure is particularly puzzling. Whereas the diffusivity anomaly observed in experiments has been reproduced in several computer studies, the parallel viscosity anomaly has received less attention. Here we simulate viscosity and the self-diffusion coefficient of the TIP4P/2005 water model over a broad temperature and pressure range. We reproduce the experimental behavior and find additional anomalies at negative pressure. The anomalous effect of pressure on dynamic properties becomes more pronounced upon cooling, reaching two orders of magnitude for viscosity at 220 K. We analyze our results with a dynamic extension of a thermodynamic two-state model, an approach which has proved successful in describing experimental data. Water is regarded as a mixture of interconverting species with contrasting dynamic behaviors, one being strong (Arrhenius) and the other fragile (non-Arrhenius). The dynamic parameters of the two-state models are remarkably close between experiment and simulations. The larger pressure range accessible to simulations suggests a modification of the dynamic two-state model, which in turn also improves the agreement with experimental data. Furthermore, our simulations demonstrate the decoupling between viscosity η and self-diffusion coefficient D as a function of temperature T. The Stokes-Einstein relation, which predicts a constant Dη/T, is violated when T is lowered, in connection with the Widom line defined by an equal fraction of the two interconverting species. These results provide a unifying picture of thermodynamics and dynamics in water and call for experiments at negative pressure.

Viscosity of deeply supercooled water and its coupling to molecular diffusion.

The viscosity of a liquid measures its resistance to flow, with consequences for hydraulic machinery, locomotion of microorganisms, and flow of blood in vessels and sap in trees. Viscosity increases dramatically upon cooling, until dynamical arrest when a glassy state is reached. Water is a notoriously poor glassformer, and the supercooled liquid crystallizes easily, making the measurement of its viscosity a challenging task. Here we report viscosity of water supercooled close to the limit of homogeneous crystallization. Our values contradict earlier data. A single power law reproduces the 50-fold variation of viscosity up to the boiling point. Our results allow us to test the Stokes-Einstein and Stokes-Einstein-Debye relations that link viscosity, a macroscopic property, to the molecular translational and rotational diffusion, respectively. In molecular glassformers or liquid metals, the violation of the Stokes-Einstein relation signals the onset of spatially heterogeneous dynamics and collective motions. Although the viscosity of water strongly decouples from translational motion, a scaling with rotational motion remains, similar to canonical glassformers.

Two-structure thermodynamics for the TIP4P/2005 model of water covering supercooled and deeply stretched regions.

One of the most promising frameworks for understanding the anomalies of cold and supercooled water postulates the existence of two competing, interconvertible local structures. If the non-ideality in the Gibbs energy of mixing overcomes the ideal entropy of mixing of these two structures, a liquid-liquid phase transition, terminated at a liquid-liquid critical point, is predicted. Various versions of the "two-structure equation of state" (TSEOS) based on this concept have shown remarkable agreement with both experimental data for metastable, deeply supercooled water and simulations of molecular water models. However, existing TSEOSs were not designed to describe the negative pressure region and do not account for the stability limit of the liquid state with respect to the vapor. While experimental data on supercooled water at negative pressures may shed additional light on the source of the anomalies of water, such data are very limited. To fill this gap, we have analyzed simulation results for TIP4P/2005, one of the most accurate classical water models available. We have used recently published simulation data, and performed additional simulations, over a broad range of positive and negative pressures, from ambient temperature to deeply supercooled conditions. We show that, by explicitly incorporating the liquid-vapor spinodal into a TSEOS, we are able to match the simulation data for TIP4P/2005 with remarkable accuracy. In particular, this equation of state quantitatively reproduces the lines of extrema in density, isothermal compressibility, and isobaric heat capacity. Contrary to an explanation of the thermodynamic anomalies of water based on a "retracing spinodal," the liquid-vapor spinodal in the present TSEOS continues monotonically to lower pressures upon cooling, influencing but not giving rise to density extrema and other thermodynamic anomalies.

Anomalies in bulk supercooled water at negative pressure.

Water anomalies still defy explanation. In the supercooled liquid, many quantities, for example heat capacity and isothermal compressibility κT, show a large increase. The question arises if these quantities diverge, or if they go through a maximum. The answer is key to our understanding of water anomalies. However, it has remained elusive in experiments because crystallization always occurred before any extremum is reached. Here we report measurements of the sound velocity of water in a scarcely explored region of the phase diagram, where water is both supercooled and at negative pressure. We find several anomalies: maxima in the adiabatic compressibility and nonmonotonic density dependence of the sound velocity, in contrast with a standard extrapolation of the equation of state. This is reminiscent of the behavior of supercritical fluids. To support this interpretation, we have performed simulations with the 2005 revision of the transferable interaction potential with four points. Simulations and experiments are in near-quantitative agreement, suggesting the existence of a line of maxima in κT (LMκT). This LMκT could either be the thermodynamic consequence of the line of density maxima of water [Sastry S, Debenedetti PG, Sciortino F, Stanley HE (1996) Phys Rev E 53:6144-6154], or emanate from a critical point terminating a liquid-liquid transition [Sciortino F, Poole PH, Essmann U, Stanley HE (1997) Phys Rev E 55:727-737]. At positive pressure, the LMκT has escaped observation because it lies in the "no man's land" beyond the homogeneous crystallization line. We propose that the LMκT emerges from the no man's land at negative pressure.