Surface Tension of Supercooled Water Determined by Using a Counterpressure Capillary Rise Method

Second inflection point of supercooled water surface tension induced by hydrogen bonds: A molecular-dynamics study

Surface tension of supercooled water is a fundamental property in various scientific processes. In this study, we perform molecular dynamics simulations with the TIP4P-2005 model to investigate the surface tension of supercooled water down to 220 K. Our results show a second inflection point (SIP) in the surface tension at temperature TSIP ≈ 267.5 ± 2.3 K. Using an extended IAPWS-E functional fit for the water surface tension, we calculate the surface excess internal-energy and entropy terms of the excess Helmholtz free energy. Similar to prior studies [Wang et al., Phys. Chem. Chem. Phys. 21, 3360 (2019); Gorfer et al., J. Chem. Phys. 158, 054503 (2023)], our results show that the surface tension is governed by two driving forces: a surface excess entropy change above the SIP and a surface excess internal-energy change below it. We study hydrogen-bonding near the SIP because it is the main cause of water's anomalous properties. With decreasing temperature, our results show that the entropy contribution to the surface tension reaches a maximum slightly below the SIP and then decreases. This is because the number of hydrogen bonds increases more slowly below the SIP. Moreover, the strengths and lifetimes of the hydrogen bonds also rise dramatically below the SIP, causing the internal-energy term to dominate the excess surface free energy. Thus, the SIP in the surface tension of supercooled TIP4P-2005 water is associated with an increase in the strengths and lifetimes of hydrogen bonds, along with a decrease in the formation rate (#/K) of new hydrogen bonds.

Machine learning (ML)-assisted surface tension and oscillation-induced elastic modulus studies of oxide-coated liquid metal (LM) alloys

Pendant drops of oxide-coated high-surface tension fluids frequently produce perturbed shapes that impede interfacial studies. Eutectic gallium indium or Galinstan are high-surface tension fluids coated with a ∼5 nm gallium oxide (Ga2O3) film and falls under this fluid classification, also known as liquid metals (LMs). The recent emergence of LM-based applications often cannot proceed without analyzing interfacial energetics in different environments. While numerous techniques are available in the literature for interfacial studies- pendant droplet-based analyses are the simplest. However, the perturbed shape of the pendant drops due to the presence of surface oxide has been ignored frequently as a source of error. Also, exploratory investigations of surface oxide leveraging oscillatory pendant droplets have remained untapped. We address both challenges and present two contributing novelties- (a) by utilizing the machine learning (ML) technique, we predict the approximate surface tension value of perturbed pendant droplets, (ii) by leveraging the oscillation-induced bubble tensiometry method, we study the dynamic elastic modulus of the oxide-coated LM droplets. We have created our dataset from LM's pendant drop shape parameters and trained different models for comparison. We have achieved >99% accuracy with all models and added versatility to work with other fluids. The best-performing model was leveraged further to predict the approximate values of the nonaxisymmetric LM droplets. Then, we analyzed LM's elastic and viscous moduli in air, harnessing oscillation-induced pendant droplets, which provides complementary opportunities for interfacial studies alternative to expensive rheometers. We believe it will enable more fundamental studies of the oxide layer on LM, leveraging both symmetric and perturbed droplets. Our study broadens the materials science horizon, where researchers from ML and artificial intelligence domains can work synergistically to solve more complex problems related to surface science, interfacial studies, and other studies relevant to LM-based systems.

Properties of water and argon clusters developed in supersonic expansions

Using adiabatic molecular dynamics coupled with the fluid dynamics equations, we model nucleation in an expanding beam of water vapor and argon on a microsecond scale. The size distribution of clusters, their temperature, and pickup cross sections in dependence on velocity are investigated and compared to the geometric cross sections and the experiment. The clusters are warmer than the expanding gas because of the time scale of relaxation processes. We also suggest that their translational and rotational kinetic energies are modified due to evaporative cooling. The pickup cross sections determined for the final clusters using molecules of the same kind increase with decreasing velocity, still obeying the (a+bN1/3)2 law.

High-density liquid (HDL) adsorption at the supercooled water/vapor interface and its possible relation to the second surface tension inflection point

We investigate the properties of water along the liquid/vapor coexistence line in the supercooled regime down to the no-man's land. Extensive molecular dynamics simulations of the TIP4P/2005 liquid/vapor interface in the range 198-348 K allow us to locate the second surface tension inflection point with a high accuracy at 283 ± 5 K, close to the temperature of maximum density. This temperature also coincides with the appearance of a density anomaly at the interface known as the apophysis. We relate the emergence of the apophysis to the observation of high-density liquid (HDL) water adsorption in the proximity of the liquid/vapor interface.

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.

Polarizable Water Potential Derived from a Model Electron Density

A new empirical potential for efficient, large scale molecular dynamics simulation of water is presented. The HIPPO (Hydrogen-like Intermolecular Polarizable POtential) force field is based upon the model electron density of a hydrogen-like atom. This framework is used to derive and parametrize individual terms describing charge penetration damped permanent electrostatics, damped polarization, charge transfer, anisotropic Pauli repulsion, and damped dispersion interactions. Initial parameter values were fit to Symmetry Adapted Perturbation Theory (SAPT) energy components for ten water dimer configurations, as well as the radial and angular dependence of the canonical dimer. The SAPT-based parameters were then systematically refined to extend the treatment to water bulk phases. The final HIPPO water model provides a balanced representation of a wide variety of properties of gas phase clusters, liquid water, and ice polymorphs, across a range of temperatures and pressures. This water potential yields a rationalization of water structure, dynamics, and thermodynamics explicitly correlated with an ab initio energy decomposition, while providing a level of accuracy comparable or superior to previous polarizable atomic multipole force fields. The HIPPO water model serves as a cornerstone around which similarly detailed physics-based models can be developed for additional molecular species.

Molecular dynamics study of wetting of alkanes on water: from high temperature to the supercooled region and the influence of second inflection points of interfacial tensions

To explore the wetting behavior of alkanes on bulk water interfaces, molecular dynamics (MD) simulations were carried out for united-atom PYS alkane models, and for SPC/E and TIP4P/2005 water models over a wide temperature range. The MD results at each temperature were used to find (1) the surface tension of the alkanes (octane, nonane) and water, and (2) the interfacial tensions of the alkane-water systems. These quantities were then used to calculate the spreading coefficient (S) and contact angle (θc) for each alkane on water. At higher temperatures, the contact angle of octane and nonane on water is found to behave in accord with conventional expectations, i.e., it decreases with increasing temperature for both water models as each system approaches the usual high-temperature transition to perfect wetting. At lower temperatures, we found an unusual temperature dependence of S and θc for each PYS alkane on SPC/E water. In contrast to conventional expectations, θc decreases with a decrease in the temperature. For octane-SPC/E water, this unusual behavior of θc occurs due to the presence of second inflection points (SIP) in the vapor-water and the octane-water interfacial tensions, whereas the SIP effect is much less important for the nonane-water system. The unusual temperature dependence of θc observed for nonane on SPC/E water is also found for nonane on TIP4P/2005 water. On the other hand, such unusual wetting behavior has not been observed in the PYS octane-TIP4P/2005 water system, except possibly for the two lowest temperatures studied.

Possible Anomaly in the Surface Tension of Supercooled Water: New Experiments at Extreme Supercooling down to -31.4 °C

The surface tension of water is suspected to show a substantial increase at low temperatures, which is considered to be one of the many anomalies of water. The second inflection point (SIP) anomaly, originally claimed to be at around -8 °C, was experimentally refuted down to -25 °C by Hrubý et al. (J. Phys. Chem. Lett. 2014, 5, 425-428). Recent molecular simulations predict the SIP anomaly near or even below the homogeneous freezing limit of around -38 °C. To contribute to an ongoing discussion about the SIP anomaly, new experiments focused on extreme levels of supercooling were carried out in this study. Unique experimental data down to -31.4 °C were collected using two measuring techniques based on the capillary rise method. A significant deviation from the extrapolated IAPWS formulation R1-76(2014) for surface tension of ordinary water was detected below -20 °C. Contrary to previous data, new experiments provide room for an anomaly in the course of surface tension in the deeply supercooled region.

Fluctuation spectroscopy of surface melting of ice with and without impurities

Water is ubiquitous, and the surface properties of ice have been studied for some time, due to their importance. A liquidlike layer (LLL) is known to exist on ice, below the melting point. We use surface thermal fluctuation spectroscopy to study the LLL, including its thickness, for pure ice, and for ice with impurities. We find that the properties of the LLL are experimentally those of liquid water, with thickness much smaller than previous results. We also find that impurities cause the LLL to be thicker, and quite inhomogeneous, with properties depending on the dopant.

Second inflection point of water surface tension in the deeply supercooled regime revealed by entropy anomaly and surface structure using molecular dynamics simulations

The surface tension of supercooled water is of fundamental importance in physical chemistry and materials and atmospheric sciences. Controversy, however, exists over its temperature dependence in the supercooled regime, especially on the existence of the "second inflection point (SIP)". Here, we use molecular dynamics simulations of the SPC/E water model to study the surface tension of water (σw) as a function of temperature down to 198.15 K, and find a minimum point of surface excess entropy per unit area around ∼240-250 K. Additional simulations with the TIP4P/2005 water model also show consistent results. Hence, we predict an SIP of σw roughly in this region, at the boundary where the "no man's land" happens. The increase of surface entropy with decreasing temperature in the region below the inflection point is clearly an anomalous behavior, unknown for simple liquids. Furthermore, we find that σw has a near-linear correlation with the interfacial width, which can be well explained by the capillary wave theory. Deep in the supercooled regime, a compact water layer at the interface is detected in our simulations, which may be a key component that contributes to the deviation of surface tension from the International Association for the Properties of Water and Steam relationship. Our findings may advance the understanding of the origin of the anomalous properties of liquid water in the supercooled regime.

Volatility of Amorphous Solid Water

Amorphous solid water is probably the most abundant form of solid water in the universe. Its saturation vapor pressure and thermodynamic properties, however, are not well known. We have investigated the saturation vapor pressure over vapor-deposited amorphous ice at temperatures between 133 and 147 K using a novel experimental method. The new method determines the absolute vapor pressures and the sublimation rates by measuring the mass growth rates of ice-covered nanoparticles under supersaturated water vapor conditions. We find that the vapor pressure of amorphous solid water is up to a factor of 3 higher than that predicted by current parameterizations, which are based in part on calorimetric measurements. We demonstrate that the calorimetric measurements can be reconciled with our data by acknowledging the formation of nanocrystalline ice as an intermediate ice phase during the crystallization of amorphous ice. As a result, we propose a new value for the enthalpy of crystallization of amorphous solid water of Δ H = 2312 ± 227 J/mol, which is about 1000 J/mol higher than the current consensus. Our results shine a new light on the abundance of water ice clouds on Mars and mesospheric clouds on Earth and may alter our understanding of ice formation in the stratosphere.

Surface tension of aqueous binary mixtures under the supercooled conditions – Development of the measuring technique and preliminary data for water + lower alcohols

An experimental apparatus originally developed for the measurement of surface tension of supercooled water was modified such that it allows for measurement of binary aqueous mixtures. The measuring principle based on the capillary rise technique is similar to that employed in the previous measurements with pure water [J. Hrubý et al., J. Phys. Chem. Lett. 5 (2014) 425 and V. Vinš et al., J. Phys. Chem. B 119 (2015) 5567]. The temperature dependence of the surface tension is determined from the measured height of the liquid column elevated in a vertical capillary tube with an inner diameter of 0.32 mm. The aqueous liquid rises to a height of 60 mm to 95 mm depending on the solute concentration and the temperature. Preliminary tests performed with the binary mixtures of water with methanol, ethanol, and n-propanol at various concentrations and temperatures down to –28 °C approved functionality of the measuring technique. Some difficulties, such as influence of impurities on the liquid column elevation or formation of bubbles in the liquid column, were observed. The experimental apparatus is further being modified in order to obtain more accurate data for various aqueous mixtures.

Ice nucleation triggered by negative pressure

Homogeneous ice nucleation needs supercooling of more than 35 K to become effective. When pressure is applied to water, the melting and the freezing points both decrease. Conversely, melting and freezing temperatures increase under negative pressure, i.e. when water is stretched. This study presents an extrapolation of homogeneous ice nucleation temperatures from positive to negative pressures as a basis for further exploration of ice nucleation under negative pressure. It predicts that increasing negative pressure at temperatures below about 262 K eventually results in homogeneous ice nucleation while at warmer temperature homogeneous cavitation, i. e. bubble nucleation, dominates. Negative pressure occurs locally and briefly when water is stretched due to mechanical shock, sonic waves, or fragmentation. The occurrence of such transient negative pressure should suffice to trigger homogeneous ice nucleation at large supercooling in the absence of ice-nucleating surfaces. In addition, negative pressure can act together with ice-inducing surfaces to enhance their intrinsic ice nucleation efficiency. Dynamic ice nucleation can be used to improve properties and uniformity of frozen products by applying ultrasonic fields and might also be relevant for the freezing of large drops in rainclouds.

Experimental and Numerical Study of the Evaporation of Water at Low Pressures

Although evaporation is considered to be a surface phenomenon, the rate of molecular transport across a liquid-vapor boundary is strongly dependent on the coupled fluid dynamics and heat transfer in the bulk fluids. Recent experimental thermocouple measurements of the temperature field near the interface of evaporating water into its vapor have begun to show the role of heat transfer in evaporation. However, the role of fluid dynamics has not been explored sufficiently. Here, we have developed a mathematical model to describe the coupling of the heat, mass, and momentum transfer in the fluids with the transport phenomena at the interface. The model was used to understand the experimentally obtained velocity field in the liquid and temperature profiles in the liquid and vapor, in evaporation from a concave meniscus for various vacuum pressures. By using the model, we have shown that an opposing buoyancy flow suppressed the thermocapillary flow in the liquid during evaporation at low pressures in our experiments. As such, in the absence of thermocapillary convection, the evaporation is controlled by heat transfer to the interface, and the predicted behavior of the system is independent of choosing between the existing theoretical expressions for evaporation flux. Furthermore, we investigated the temperature discontinuity at the interface and confirmed that the discontinuity strongly depends on the heat flux from the vapor side, which depends on the geometrical shape of the interface.

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.

Abnormal gas-liquid-solid phase transition behaviour of water observed with in situ environmental SEM

Gas-liquid-solid phase transition behaviour of water is studied with environmental scanning electron microscopy for the first time. Abnormal phenomena are observed. At a fixed pressure of 450 Pa, with the temperature set to −7 °C, direct desublimation happens, and ice grows continuously along the substrate surface. At 550 Pa, although ice is the stable phase according to the phase diagram, metastable liquid droplets first nucleate and grow to ~100–200 μm sizes. Ice crystals nucleate within the large sized droplets, grow up and fill up the droplets. Later, the ice crystals grow continuously through desublimation. At 600 Pa, the metastable liquid grows quickly, with some ice nuclei floating in it, and the liquid-solid coexistence state exists for a long time. By lowering the vapour pressure and/or increasing the substrate temperature, ice sublimates into vapour phase, and especially, the remaining ice forms a porous structure due to preferential sublimation in the concave regions, which can be explained with surface tension effect. Interestingly, although it should be forbidden for ice to transform into liquid phase when the temperature is well below 0 °C, liquid like droplets form during the ice sublimation process, which is attributed to the surface tension effect and the quasiliquid layers.

Possible Evidence for a New Form of Liquid Buried in the Surface Tension of Supercooled Water

Contrary to the historical data, several recent experiments indicate that the surface tension of supercooled water follows a smooth extrapolation of the IAPWS equation in the supercooled regime. It can be seen, however, that a small deviation from the IAPWS equation is present in the recent experimental measurements. It is shown with simulations using the WAIL water potential that the small deviation in the experimental data is consistent with the tail of an exponential growth in surface tension as temperature decreases. The emergence temperature, Te, of a substantial deviation from the IAPWS equation is shown to be 227 K for the WAIL water and 235 K for real water. Since the 227 K Te is close to the Widom line in WAIL water, we argue that real water at 235 K approaches a similar crossover line at one atmospheric pressure.