Significance The importance of molecular understanding of the structure, dynamics. and properties of liquid water is recognized in many scientific disciplines. Here, we study experimentally the structure and thermodynamics of bulk liquid water as it is supercooled by evaporation down to ∼228 K. The unique aspect of this work is the use of ultrafast calorimetry that enables us to determine the specific-heat capacity of water to unprecedentedly low temperatures. The observed maximum of about 218 J/mol/K at 229 K is consistent with the liquid–liquid critical point model and supports a proposed fragile-to-strong transition at ∼220 K to explain the steep decrease in the estimated self-diffusion coefficient below 235 K. Knowledge of the temperature dependence of the isobaric specific heat (Cp) upon deep supercooling can give insights regarding the anomalous properties of water. If a maximum in Cp exists at a specific temperature, as in the isothermal compressibility, it would further validate the liquid–liquid critical point model that can explain the anomalous increase in thermodynamic response functions. The challenge is that the relevant temperature range falls in the region where ice crystallization becomes rapid, which has previously excluded experiments. Here, we have utilized a methodology of ultrafast calorimetry by determining the temperature jump from femtosecond X-ray pulses after heating with an infrared laser pulse and with a sufficiently long time delay between the pulses to allow measurements at constant pressure. Evaporative cooling of ∼15-µm diameter droplets in vacuum enabled us to reach a temperature down to ∼228 K with a small fraction of the droplets remaining unfrozen. We observed a sharp increase in Cp, from 88 J/mol/K at 244 K to about 218 J/mol/K at 229 K where a maximum is seen. The Cp maximum is at a similar temperature as the maxima of the isothermal compressibility and correlation length. From the Cp measurement, we estimated the excess entropy and self-diffusion coefficient of water and these properties decrease rapidly below 235 K.

The well-known classical nucleation theory (CNT) for the free energy barrier towards formation of a nucleus of critical size of the new stable phase within the parent metastable phase fails to take into account the influence of other metastable phases having density/order intermediate between the parent metastable phase and the final stable phase. This lacuna can be more serious than capillary approximation or spherical shape assumption made in CNT. This issue is particularly significant in ice nucleation because liquid water shows rich phase diagram consisting of two (high and low density) liquid phases in supercooled state. The explanations of thermodynamic and dynamic anomalies of supercooled water often invoke the possible influence of a liquid-liquid transition between two metastable liquid phases. To investigate both the role of thermodynamic anomalies and presence of distinct metastable liquid phases in supercooled water on ice nucleation, we employ density functional theoretical approach to find nucleation free energy barrier in different regions of phase diagram. The theory makes a number of striking predictions, such as a dramatic lowering of nucleation barrier due to presence of a metastable intermediate phase and crossover in the dependence of free energy barrier on temperature near liquid-liquid critical point. These predictions can be tested by computer simulations as well as by controlled experiments.

Mounting experimental evidence supports the existence of a liquid-liquid transition (LLT) in high-pressure supercooled water. However, fast crystallization of supercooled water has impeded identification of the LLT line <i>T</i>_LL(<i>p</i>) in experiments. While the most accurate all-atom (AA) water models display a LLT, their computational cost limits investigations of its interplay with ice formation. Coarse-grained (CG) models provide over 100-fold computational efficiency gain over AA models, enabling the study of water crystallization, but have not yet shown to have a LLT. Here, we demonstrate that the CG machine-learned water model Machine-Learned Bond-Order Potential (ML-BOP) has a LLT that ends in a critical point at <i>p</i>_c = 170 ± 10 MPa and <i>T</i>_c = 181 ± 3 K. The <i>T</i>_LL(<i>p</i>) of ML-BOP is almost identical to the one of TIP4P/2005, adding to the similarity in the equation of state of liquid water in both models. Cooling simulations reveal that ice crystallization is fastest at the LLT and its supercritical continuation of maximum heat capacity, supporting a mechanistic relationship between the structural transformation of water to a low-density liquid (LDL) and ice formation. We find no signature of liquid-liquid criticality in the ice crystallization temperatures. ML-BOP replicates the competition between formation of LDL and ice observed in ultrafast experiments of decompression of the high-density liquid (HDL) into the region of stability of LDL. The simulations reveal that crystallization occurs prior to the coarsening of the HDL and LDL domains, obscuring the distinction between the highly metastable first-order LLT and pronounced structural fluctuations along its supercritical continuation.

Robust thermodynamic data are essential for the development of geodynamic and geochemical models of ocean worlds. The water–ammonia system is of interest in the study of ocean worlds due to its purported abundance in the outer solar system, geological implications, and potential importance for origins of life. In support of developing new equations of state, we conducted 1 bar specific heat capacity measurements (Cp) using a differential scanning calorimeter (DSC) at low temperatures (184–314 K) and low mass fractions of ammonia (5.2–26.9 wt %) to provide novel data in the parameter space most relevant for planetary studies. This is the first known set of data with sufficient fidelity to investigate the trend of specific heat capacity with respect to temperature. The obtained Cp in the liquid phase domain above the liquidus generally increases with temperature. Deviations of our data from the currently adopted equation of state by Tillner-Roth and Friend[Tillner-RothR.; FriendD. G.J. Phys. Chem. Ref. Data1998, 27, 63–96]. are generally negative (ranging from +1 to −10%) and larger at lower temperatures. This result suggests that suppression of the critical behavior of supercooled water (rapid increase in specific heat with decreasing temperature) by ammonia starts at a smaller concentration than that set by Tillner-Roth and Friend.[Tillner-RothR.; FriendD. G.J. Phys. Chem. Ref. Data1998, 27, 63–96]. Cp measurements of the liquid were also obtained in the partial melting domain between the eutectic and liquidus. This novel data set will be useful in future investigations of conditions where such partial melt may exist, such as the ice shell–ocean boundary or the interiors of ocean worlds that may contain relatively large proportions of dissolved ammonia.

We performed small-angle x-ray scattering measurements of liquid Te using a synchrotron radiation facility and observed maximum scattering intensity near 620 K in the supercooled region (melting temperature 723 K). This indicates that density inhomogeneity exists in liquid Te, and the fact that this temperature coincides with the temperature at which the specific heat, sound velocity, and thermal expansion coefficient reach their maxima means that this density inhomogeneity is the cause of these thermodynamic anomalies. The thermodynamic anomalies in liquid Te had already been shown in the 1980s to be comprehensively explained by the inhomogeneity associated with the continuous liquid–liquid phase transition (LLT), but direct experimental evidence for the existence of the inhomogeneity had not been obtained. The present results, together with those already obtained for mixture systems (Te–Se, Te–Ge), indicate the existence of inhomogeneity associated with LLT in liquid Te systems, and strongly support the model. Recently, similar maximum scattering intensity has also been observed in supercooled liquid water, which exhibits thermodynamic anomalies similar to those of Te, indicating the universality of the inhomogeneous model or LLT scenario to explain the thermodynamics of such 'anomalous liquids'. Further development of the LLT scenario is expected in near future.

Numerous anomalies of water have been reported in the literature. Anomalous behaviour of liquid water is so striking when it is supercooled below the melting temperature of ice, Tm. Several physical properties have been found to be diverging in the supercooled liquid phase, including isobaric heat capacity, isothermal compressibility, relaxation time and thermal expansion coefficient. Interestingly hydrogen bond life times show a divergence at this temperature, indicating its connection to these singularities. Liquid water exhibits both density maximum and minimum, the latter has been discovered by a recent Small Angle Neutron Scattering (SANS) experiments, considered to be two of its most notable thermodynamic anomalies. Unlike other liquids, translational and diffusive motions in water exhibit contrasting behaviour and product of these two diffusive constants is found to be insensitive to temperature and density. Formation of water clusters of varying sizes dictates the nature of diffusion in supercooled water. Several propositions have been made in order to account for water’s anomalies, which include Liquid−Liquid Critical Point theory, Singularity Free hypothesis, Critical Point−Free hypothesis and Stability Limit conjecture. In bulk phase, water shows its most of the anomalies. In addition, it exhibits several other anomalous characters when confined to nanoscale geometries and is near to macromolecular surface. It has to be noted that in the vicinity of non−polar solut

THE metastable extension of the phase diagram of liquid water exhibits rich features that manifest themselves in the equilibrium properties of water. For example, the density maximum at 4 °C and the minimum in the isothermal compressibility at 46 °C are thought to reflect the presence of singularities in the behaviour of thermodynamic quantities occurring in the supercooled region1 2. The 'stability–limit conjecture'3–5 suggests that these thermodynamic anomalies arise from a single limit of mechanical stability (spinodal line), originating at the liquid–gas critical point, which determines the limit of both superheating at high temperatures and supercooling at low temperatures. Here we present a comprehensive series of molecular dynamics simulations which suggest that, instead, the supercooling anomalies are caused by a newly identified critical point, above which the two metastable amorphous phases of ice (previously shown to be separated by a line of first-order transitions6,7) become indistinguishable. The two amorphous ice phases are thus incorporated into our understanding of the liquid state, providing a more complete picture of the metastable and stable behaviour of water.

For the last 50 years, researchers have sought molecular models that can accurately reproduce water’s microscopic structure and thermophysical properties across broad ranges of its complex phase diagram. Herein, molecular dynamics simulations with the many-body MB-pol model are performed to monitor the thermodynamic response functions and local structure of liquid water from the boiling point down to deeply supercooled temperatures at ambient pressure. The isothermal compressibility and isobaric heat capacity show maxima near 223 K, in excellent agreement with recent experiments, and the liquid density exhibits a minimum at ~208 K. A local tetrahedral arrangement, where each water molecule accepts and donates two hydrogen bonds, is found to be the most probable hydrogen-bonding topology at all temperatures. This work suggests that MB-pol may provide predictive capability for studies of liquid wa- ter’s physical properties across broad ranges of thermodynamic states, including the so-called water’s “no man’s land” which is difficult to probe experimentally.

We report an experimental observation of mesoscopic fluctuations underlying the thermodynamic anomalies of ambient liquid water. The combination of two sound-velocity-measurement methods with largely different frequencies, namely inelastic x-ray scattering (IXS) in the terahertz band and ultrasonic (US) in the megahertz band, allows us to investigate a relaxation phenomenon that has a characteristic frequency between the two aforementioned frequencies. We performed IXS measurements to obtain the IXS sound velocity of liquid water from the ambient conditions to the supercritical region of liquid–gas phase transition (LGT) and compared the results with the US sound velocity reported in the literature. We found that the ratio of the sound velocities, S_{f}, which corresponds to the relaxation strength, obtained using these two methods exhibits a simple but significant change. Two distinct rises were observed in the high- and low-temperature regions, implying that two relaxation phenomena exist. In the high-temperature region, a peak was observed near the LGT critical ridge line, which was linked to changes in the magnitude of density fluctuation and isochoric and isobaric-specific heat capacities. This result indicates that the high-temperature relaxation originates from the LGT critical fluctuation, proving that this method is effective for observing such mesoscopic fluctuations. Meanwhile, in the low-temperature region, S_{f} increased from 550 K toward the low-temperature reg

A Bragg X-ray spectrometer equipped with a volume-sensitive Geiger counter and Soller slits and employing filtered molybdenum Ka radiation was used to obtain a set of diffracted intensity curves as a Punction of angle for supercooled water. Diffracted intensity curves in the temperature region of 21 to -16 C were obtained. The minimum between the two main diffraction peaks deepened continuously with lowering temperature, indicating a gradual change in the internal structure of the water. No discontinuity in this trend was noted at the melting point. The internal structure of supercooled water was concluded to become progressively more ice-like as the temperature is lowered.

The process by which liquid cloud droplets homogeneously crystallize into ice is still not well-understood. The ice nucleation process based on the standard and classical theory of homogeneous freezing, initiates within the interior volume of a cloud droplet. Current experimental data on homogeneous freezing rates of ice in droplets of supercooled water, both in air and emulsion oil samples, show considerable scatter. For example, at -33 C, the reported volume-based freezing rates of ice in supercooled water vary by as much as 5 orders of magnitude, which is well outside the range of measurement uncertainties. Here, we show that the process of ice nucleus formation at the air (or oil)-liquid water interface may help to explain why experimental results on ice nucleation rates yield different results in different ambient phases. Our results also suggest that surface crystallization of ice in cloud droplets can explain why low amounts of supercooled water have been observed in the atmosphere near -40 C.