Thermodynamics and dynamics of supercooled water
Stokely, Kevin C
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This thesis utilizes the methods of statistical physics and computer simulation to study the thermodynamic and dynamic behavior of liquid water at supercooled temperatures. The behavior of water deviates from that of a simple liquid in a number of remarkable ways, many of which become more apparent as the liquid is supercooled below its equilibrium freezing temperature. Yet, due to nucleation to the crystalline state, a large region of the phase diagram of the supercooled liquid remains unexplored. We make use of a simple model for liquid water to shed light on the behavior of real water in the experimentally inaccessible region. The model predicts a line of phase transitions in the pressure--temperature plane, between high- and low- density forms of liquid water, ending in a liquid-liquid critical point (LLCP). Such a LLCP provides a thermodynamic origin for one of liquid water's anomalies--the rapid rise, and extrapolated divergence, of thermodynamic response functions upon cooling. We find one such response function, the isobaric specific heat, CP, displays two distinct maxima as a function of temperature T in the supercooled region. One maximum is a consequence of the directional nature of hydrogen (H) bonding among molecules; the other is a consequence of the cooperative nature of H bonding. With pressurization, these two maxima move closer in T, finally coinciding at the LLCP. This suggests that measurement of CP far from any LLCP could provide evidence for the existence of water's LLCP. Recent experiments find that the T-dependence of the characteristic time for H bond rearrangement displays three distinct regimes. Our observed behavior of CP, combined with Adam-Gibbs theory, allows for a thermodynamic interpretation of this feature of water's dynamics. The dynamics of the model are also measured directly by a Monte Carlo procedure, and are found in agreement with experiment. Further, the model allows the directional and cooperative components of the H bond interaction to be varied independently. By varying only these two energy scales, the low-T phase diagram changes dramatically, exhibiting one of several previously proposed thermodynamic scenarios. Our results link each of these scenarios, by recognizing the energetics of the H bond as the underlying physical mechanism responsible for each.
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