Thermodynamic Properties Of Supercooled Water Research Articles

Thermodynamic picture of vitrification of water through complex specific heat and entropy: A journey through "no man's land".

We investigate thermodynamic properties of supercooled water across the "no man's land" onto the formation of amorphous ice. The calculations are aided by very long computer simulations, often more than 50 μs long, with the TIP4P/2005 model potential. Density fluctuations that arise from the proximity to a putative liquid-liquid (LL) transition at 228 K, cast a long shadow on the properties of water, both above and below the LL transition. We carry out the calculations of the quantum mechanical static and frequency-dependent specific heats by combining seminal studies of Lebowitz, Percus, and Verlet and Grest and Nagel with the harmonic approximation for the density of states. The obtained values are in quantitative agreement with all available experimental and numerical results of specific heats for both supercooled water and ice. We calculate the entropy at all the state points by integrating the specific heat. We find that the quantum corrected-contributions of intermolecular vibrational entropy dominate the excess entropy of amorphous phases over the crystal over a wide range of temperatures. Interestingly, the vibrational entropy lowers the Kauzmann temperature, TK, to 130 K, just below the experimental glass-to-liquid water transition temperature, Tg, of 136 K and the calculated Tg of 135 K in our previous study. A straightforward extrapolation of high temperature entropy from 250 K to below however would give a much higher value of TK ∼ 190 K. The calculation of Lindemann ratios shows the melting of amorphous ice ∼135 K. The amorphous state exhibits an extremely short correlation length for the distance dependence of orientational correlation.

Thermodynamics of Liquid–Liquid Criticality in Supercooled Water in a Mean-Field Approximation

In a recent publication, it has been shown how a non-analytic scaling theory of critical phenomena can describe the available experimental information for the thermodynamic properties of supercooled water, when it is assumed to exhibit a liquid–liquid critical point. In this article, we present a mean-field equation of state which also represents the experimental data for supercooled water. Compared to the scaling theory, the mean-field equation has the advantage of simplicity for practical calculations of the properties of supercooled water. The insensitivity to a particular form of a critical equation of state is due to a lack of experimental data asymptotically close to the liquid–liquid critical point. Hence, while the assumed existence of a liquid–liquid critical point in water can account for the observed thermodynamic behavior of supercooled water, the actual location of such a liquid–liquid critical point cannot be determined accurately from the available experimental thermodynamic property data.

Absence of the Density Minimum of Supercooled Water in Hydrophobic Confinement

The surface effect on the peculiar dynamic and thermodynamic properties of supercooled water, such as the density, has been puzzling the scientific community for years. Recently, using the small angle neutron scattering method, we were able to measure the density of H(2)O confined in the hydrophobic mesoporous material CMK-1-14 from room temperature down to the deeply supercooled temperature 130 K at ambient pressure. We found that the well-known density maximum of water is shifted 17 K lower and, more interestingly, that the previously observed density minimum in hydrophilic confinement disappears. Furthermore, the deduced thermal expansion coefficient shows a much broader peak spanning from 240 to 180 K in comparison with the sharp peak at 230 K in hydrophilic confinement. These present results may help in the understanding of the effect of hydrophobic/hydrophilic interfaces on the properties of supercooled confined water.

Scaled Equation of State for Supercooled Water near the Liquid-Liquid Critical Point

We have developed a scaled parametric equation of state to describe and predict thermodynamic properties of supercooled water. The equation of state, built on the growing evidence that the critical point of supercooled liquid-liquid water separation exists, is universal in terms of theoretical scaling fields and is shown to belong to the Ising-model class of universality. The theoretical scaling fields are postulated to be analytical combinations of the physical fields, pressure, and temperature. The equation of state enables us to accurately locate the "Widom line" (the locus of stability minima) and determine that the critical pressure is considerably lower than predicted by computer simulations.

Analysis of the equations-of-state of water in the metastable region at high pressures

We analyze the existing equations-of-state of liquid water from the point of view of their applicability to equilibrium and nonequilibrium water–ice phase change problems that involve supercooled water. We show that the equation-of-state of Saul and Wagner [J. Phys. Chem. Ref. Data 18, 1537 (1989)] is most suitable for the description of thermodynamic properties of supercooled water in the range of pressures 0–200 kbar, and find the area of its validity in the metastable region.

The metastable T−P phase diagram and anomalous thermodynamic properties of supercooled water

The metastable T−P phase diagram and the anomalies of the thermodynamic properties of supercooled water are calculated on the basis of a two-level thermodynamic model. Water is considered as a mixture of two components which differ in atomic configurations and correspond to low-density amorphous (lda) and high-density amorphous (hda) ice. The expression for the Gibbs potential of water is written in the form which is analogous to that of usual regular binary solutions. But this model considers the concentration, c, of the components, as a pressure and temperature-dependent internal parameter. There are only four constants in the expression for the Gibbs potential: the differences in the specific volumes, entropies, and energies of the two components and the mixing energy of the components whose values are ΔV0=−3.8 cm3/mol, ΔS0=4.225 J/mol, ΔE0=1037 J/mol, and U=3824 J/mol, respectively. The lda−hda phase equilibrium line terminates at the critical point, Tcr=230 K and Pcr=0.173 kbar, the second critical point in the phase diagram of water. The anomalous thermal dependence of the specific volume, the heat expansion coefficient, and the specific heat of water calculated for the atmospheric pressure is in a good quantitative agreement with the available experimental data. Thus anomalous properties of supercooled water are well explained by the occurrence of the second critical point close to the atmospheric pressure. The absolute value of parameter c is not crucial for the thermal behavior of properties, instead, the anomalies in water are due to the dependence on pressure and temperature. The parameter c behavior is analyzed in various pressure and temperature ranges around the second critical point. The thermal dependence of parameter c is very weak in the temperature range of 290–350 K at atmospheric pressure. As a consequence, the thermodynamic properties of water behave in this range like those of a normal liquid though water stays a mixture of two components, lda-like and hda-like, in an approximate proportion 2:3.

Homogeneous nucleation of supercooled water: Results from a new equation of state

A series of laboratory and aircraft measurements have indicated that supercooled liquid water exists to temperatures as low as −70°C. These measurements also show that classical nucleation theory, using standard values for the thermodynamic properties of supercooled water, underestimates the nucleation rate of ice in liquid water at large supercoolings. New theoretical estimates for this homogeneous nucleation rate are presented, based on a new analytic equation of state for liquid water. The new equation of state, which is accurate over a pressure range of 3000 atmospheres and a temperature range of 1200K, is used to infer the latent heat of melting, liquid water density, and ice‐water surface energy of supercooled water. Predictions of the nucleation rate and the homogeneous freezing temperature made by this equation of state are in agreement with observations at temperatures as cold as −70°C and at pressures as high as 2000 atmospheres. These results indicate that it is not necessary to invoke a phase transition at −45°C to explain aircraft and laboratory observations of homogeneous ice nucleation in supercooled water clouds.

Thermodynamic properties of supercooled water at 1 atm

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTThermodynamic properties of supercooled water at 1 atmRobin J. SpeedyCite this: J. Phys. Chem. 1987, 91, 12, 3354–3358Publication Date (Print):June 1, 1987Publication History Published online1 May 2002Published inissue 1 June 1987https://doi.org/10.1021/j100296a049RIGHTS & PERMISSIONSArticle Views860Altmetric-Citations137LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (574 KB) Get e-Alerts