Thermodynamics supercooled water

It should be mentioned that in the last few years super-cooled water has attracted the interest of many scientists because of its exceeding properties and life at temperatures below 0 °C 1819). Speedy recently published a model which allows for the interpretation of the thermodynamic anomalies of supercooled water 20). According to this model there are hydrogen bonded pentagonal rings of water molecules which have the quality of self-replication and association with cavities. 

Sastry, S., Debenedetti, P., Sciortino, F., and Stanley, H.E. 1996. Singularity-free interpretation of the thermodynamics of supercooled water. Phys. Rev. E53, 6144-6154. 

To calculate the entropy changes, it is necessary to consider a series of reversible steps leading from liquid water at —10°C to sohd ice at —10°C. One such series might be (1) Heat supercooled water at —10°C very slowly (reversibly) to 0°C, (2) convert the water at 0°C very slowly (reversibly) to ice at 0°C, and (3) cool the ice very slowly (reversibly) from 0°C to —10°C. As each of these steps is reversible, the entropy changes can be calculated by the methods discussed previously. As S is a thermodynamic property, the sum of these entropy changes is equal to AS for the process indicated by Equation (6.97). The necessary calculations are summarized in Table 6.2, in which T2 represents 0°C and Ti represents 10°C. 

Tmskett and Dill (2002) proposed a two-dimensional water-like model to interpret the thermodynamics of supercooled water. This model is consistent with model (1) for liquid water. Cage-like and dense fluid configurations correspond to transient structured and unstructured regions, observed in molecular simulations of water (Errington and Debenedetti, 2001). Truskett and Dill s model provides a microscopic theory for the global phase behavior of water, which predicts the liquid-phase anomalies and expansion upon freezing. 

The sharing of imperfect cluster faces of the clathrate-like clusters can be viewed as a thermodynamic tendency to minimize the negative entropies of solution. The tendency for face- or edge-sharing of individual solvation clusters, as Stillinger (1980) pointed out, is the same as the tendency for clustering of pure supercooled water. 

Speedy RJ (1987) Thermodynamic properties of supercooled water at 1 atm. J Phys Chem 91 3354-3358... 

Note There are three allotropes of carbon graphite, diamond, and buckminsterfullerene (Cgo) the latter, discovered in 1985, is composed of soccer-ball-shaped molecules. The thermodynamic stability of buckminsterfullerene has not yet been determined. The validity of its inclusion on the C phase diagram is, therefore, uncertain. (Metastable phases, such as supercooled water, do not appear on phase diagrams.) The crystal structure is face-centered cubic with Ceo molecules at the corners and faces of a cubic unit cell. The unit cell is shown below. 

Simulations essentially extend possibility to study supercooled liquid water, as crystallization may be suppressed. However, there is no water model, which adequately reproduces phase diagram of water and its properties even in the thermodynamic region, where experimental data are available. In such situation, only comparative analysis of the results, obtained for various water models, can give information, relevant for the behaviour of real water in supercooled region. Additional complication appears due to the necessity to use sophisticated simulation methods, appropriate for the studies of the phase transitions, such as Monte Carlo simulations in the grand canonical or in the Gibbs ensemble (see Refs.7,16 for more details). Note, that simulations in the simple constant-volume or constant-pressure ensembles, widely used in the studies of supercooled water (see, for example Refs. 17,18), are not appropriate for the location of the phase transitions. 

Speedy, R.J. and Angell, C.A. Isothermal compressibility of supercooled water and evidence for a thermodynamic singularity at -45°C, /. Chem. Phys., 65, 851, 1976. 

In considering the kinetics of crystallization of supercooled water and representing the domelike eurve 1 for the crystallization rate we left aside the question of the spinodal of supercooled liquid. If such a spinodal exists, it means that, at least, a part of eurve 1 (on the left) does not conform to the actual possibility of nucleation in a homogeneous system. The decrease of the inverse isothermal eompressibility of water with a temperature decrease below 319 K is interpreted by the authors as a trace of thermodynamic singularity at 228 K (curve 3"). However, it does not agree with the liquid capacity for much greater supercoolings established by experiment. 

Rouch, J., Lai, C. C., Chen, C. H. (1977) High frequency sound velocity and sound absorption in supercooled water and thermodynamics singularity at 228 K. J. Chem. Phys. 66, 5031-5034... 

Enthalpy, Entropy, and Heat Capacity of Protein—Water Systems Below 0°C. A number of investigators have reported the apparent enthalpy of fusion as a function of temperature and composition for several hydrated proteins. MacKenzie and coworkers (10) determined absorption isotherms at low temperatures and found that 1) these absorption isotherms have essentially the same sigmoidal shapes as those observed above zero degrees 2) the magnitudes of the values for partial molal enthalpy and entropy increase as the content of unfrozen water decreases 3) the heat of fusion decreases as the content of unfrozen water decreases and 4) the heat capacity of the system increases as the content of unfrozen water increases. Taking these findings all together, the thermodynamic properties of unfrozen water are not very different from those of supercooled water at comparable temperatures. 

So within the insulated vessel the total entropy change is positive, in accordance with the Second Law of Thermodynamics, because the freezing of supercooled water at -5°C is a spontaneous process. (As in Example 5.1 AS sun=0, because the process is adiabatic.)... 

The role of ice in rain formation was first addressed by Bergeron in 1933, based on the calculations of Wegener. Using thermodynamics, Wegener showed in 1911 that at temperatures below 0°C supercooled water drops and ice crystals cannot exist in... 

B. Jana, R. S. Singh and B. Bagchi, String-Uke propagation of the 5-coordinated defect state in supercooled water molecular origin of dynamic and thermodynamic anomalies. Phys. Chem. Chem. Phys. 13 (2011), 16220-16226. 

Many experiments have been performed to test the various hypotheses discussed in the previous section, but there is as yet no widespread agreement on which physical picture, if any, is correct. The connection between liquid and the two amorphous forms predicted by the LLPT hypothesis is difficult to prove experimentally because supercooled water freezes spontaneously below the nucleation temperature Tw, and amorphous ice crystallizes above the crystallization temperature Tx [32,33]. Crystallization makes experimentation on the supercooled liquid state between Th and Tx almost impossible. However, comparing experimental data on amorphous ice at low temperatures with those of liquid water at higher temperatures allows an indirect discussion of the relationship between the liquid and amorphous states. It is found from neutron diffraction studies [10] and simulations that the structure of liquid water changes toward the LDA structure when the liquid is cooled at low pressures and changes toward the HDA structure when cooled at high pressures, which is consistent with the LLPT hypothesis. Because their entropies are small, the two amorphous states are presently considered to be smoothly connected thermodynamically to the liquid state [34]. 

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