Chapter 18
Phase Diagram for Supercooled Water and Liquid-Liquid Transition Downloaded by STANFORD UNIV GREEN LIBR on October 4, 2012 | http://pubs.acs.org Publication Date: September 30, 1997 | doi: 10.1021/bk-1997-0676.ch018
Hideki Tanaka Department of Polymer Chemistry, Graduate School of Engineering, Kyoto University, Sakyo, Kyoto 606-01, Japan
Molecular dynamics simulations have been carried out at constant pressure and temperature to examine phase behaviors of supercooled water. The anomalies of supercooled water in thermodynamic response functions at atmospheric pressure, the phase transition between low and high density amorphous ices (LDA and HDA) and a fragile-strong transition are accounted for by reconciling an idea introducing a second critical point separating L D A and H D A ices with a conjecture that L D A is a different phase from a normal water, called water II. It is found that there exist large gaps around temperature 213 K in thermodynamic, structural and dynamic properties, suggesting liquid-liquid phase transition. This transition is identified as an extension of the experimentally observed L D A - H D A transition in high pressure to atmospheric pressure. In a new phase diagram, a locus of the second critical point is moved into negative pressure and the divergences are accounted for in terms of the critical point and the spinodal-like instability.
Water exhibits various anomalies in thermodynamic response functions such as heat capacity and isothermal compressibility. The heat capacity at constant pressure in ambient temperature is large compared with other liquid. The isothermal compressibility has a minimum around 319 K . Below this temperature, water becomes more compressible liquid as decreasing temperature (1). Those properties in supercooled state tend to diverge with a power law behavior when approaching to Ts, 228 K (2). Before reaching the divergence temperature, water always nucleates. The experimental limit of supercooling is Ti (233 K ) at atmospheric pressure. Therefore, it is impossible to investigate experimentally what happens at molecular level near Ts. These anomalies have been accounted for by various ideas and conjectures. Among them, the most notable one was due to Speedy, which is called "stabilityhmit-conjecture" (3). He explained the divergence of thermodynamic properties in © 1997 American Chemical Society
In Supercooled Liquids; Fourkas, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1997.
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Downloaded by STANFORD UNIV GREEN LIBR on October 4, 2012 | http://pubs.acs.org Publication Date: September 30, 1997 | doi: 10.1021/bk-1997-0676.ch018
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SUPERCOOLED LIQUIDS
supercooled state in conjunction with the liquid-vapor spinodal. The liquid spinodal line begins at the liquid-gas critical point. In temperature-pressure plane, mis line decreases monotonically with decreasing temperature and goes into negative pressure. The liquid spinodal line has a minimum at negative pressure and passes back to positive pressure as the temperature decreases further. The anomalous thermodynamic behavior of liquid water in the low temperature region can be related to such a reentrant spinodal line, where the thermodynamic properties diverge like approaching to a critical point. The metastable supercooled water is necessarily changed to stable ice below this temperature according to the stability limit conjecture. Poole et al carried out molecular dynamics (MD) simulations over a wide range of stable, metastable and unstable liquid-state points to find a reentrant of the spinodal line (4). But the liquid spinodal line decreases monotonically with decreasing temperature and does not reenter into the positive pressure region. Instead, they found a second critical point. They located the second critical point at around 120 MPa and concluded that the anomalies are related to the second critical point from which an L D A (low density amorphous) - H D A (high density amorphous) phase boundary appears (5). The phase diagram they proposed suggests that if crystallization does not intervene, supercooled water is further cooled to L D A without a phase transition. L D A at 0.1 MPa is hard to be prepared by an ordinary method but can be made by hyperquenching or compres si on-decompres si on of ice. The glass transition temperature was observed at Tg, 136 K (6). L D A becomes liquid above Tg. When heated further, L D A changes to cubic ice above Ti, 150 K (7). Therefore, it is again impossible to examine the origin of the divergence from lower temperature side. A t high pressure, L D A - H D A transition was experimentally observed. It exhibits pressure-hysteresis and is therefore first order phase transition (8). M D simulations successfully reproduced this transition (9). This ensures that die intermolecular interaction for water is sufficient to describe the low temperature and high pressure behaviors of water although temperature and pressure must be shifted to some degree when compared with experiment. Speedy proposed the other conjecture that L D A has no continuous path from normal water at atmospheric pressure (10). L D A and H D A are liquid above Tg; the former is called "water II", which is a different phase from normal water. The free energy difference between L D A and ice at temperature T is assumed simply by AG (T)
