Four scenarios have been proposed for the low-temperature phase behavior of liquid water, each predicting different thermodynamics. The physical mechanism that leads to each is debated. Moreover, it is still unclear which of the scenarios best describes water, because there is no definitive experimental test. Here we address both open issues within the framework of a microscopic cell model by performing a study combining mean-field calculations and Monte Carlo simulations. We show that a common physical mechanism underlies each of the four scenarios, and that two key physical quantities determine which of the four scenarios describes water: (i) the strength of the directional component of the hydrogen bond and (ii) the strength of the cooperative component of the hydrogen bond. The four scenarios may be mapped in the space of these two quantities. We argue that our conclusions are model independent. Using estimates from experimental data for H-bond properties the model predicts that the low-temperature phase diagram of water exhibits a liquid-liquid critical point at positive pressure.anomalous liquids | liquid-liquid transition | liquid water | mean field | Monte Carlo simulations W ater's phase diagram is rich and complex: more than sixteen crystalline phases (1), and two or more glasses (2-4) have been reported. The liquid state also displays interesting behavior, such as the density maximum for 1 atm at 4°C. The volume fluctuations hðδV Þ 2 i, entropy fluctuations hðδSÞ 2 i, and cross fluctuations between volume and entropy hδV δSi, proportional to the magnitude of isothermal compressibility K T , isobaric specific heat C P , and isobaric thermal expansivity α P , respectively, show anomalous increases in magnitude upon cooling (5). Further, these quantities display an apparent divergence for 1 atm at −45°C (2), hinting at interesting phase behavior in the supercooled region.Microscopically, liquid water's anomalous behavior is understood as resulting from the tendency of neighboring molecules to form hydrogen (H) bonds upon cooling with a decrease of local potential energy, decrease of local entropy, and increase of local volume due to the formation of local open structures of bonded molecules. Different models include these H-bond features, but depending on the assumptions and approximations of each model, different conclusions are obtained for the low-T phase behavior. The relevant region of the bulk-liquid state cannot be probed experimentally, and none of the theories tested because crystallization of bulk water is unavoidable below the homogeneous nucleation temperature T H (−38°C at 1 atm). Four Scenarios for Supercooled WaterDue to the difficulty of obtaining experimental evidence, theoretical and numerical analyses are useful. Four separate scenarios for the pressure-temperature (P-T) phase diagram have been proposed: (I) The stability limit (SL) scenario (6) hypothesizes that the superheated liquid-gas spinodal at negative pressure reenters the positive P region below T H ðPÞ. In this view, the liq...
Studies of liquid water in its supercooled region have helped us better understand the structure and behavior of water. Bulk water freezes at its homogeneous nucleation temperature (approximately 235 K), but protein hydration water avoids this crystallization because each water molecule binds to a protein. Here, we study the dynamics of the hydrogen bond (HB) network of a percolating layer of water molecules and compare the measurements of a hydrated globular protein with the results of a coarse-grained model that successfully reproduces the properties of hydration water. Using dielectric spectroscopy, we measure the temperature dependence of the relaxation time of proton charge fluctuations. These fluctuations are associated with the dynamics of the HB network of water molecules adsorbed on the protein surface. Using Monte Carlo simulations and mean-field calculations, we study the dynamics and thermodynamics of the model. Both experimental and model analyses are consistent with the interesting possibility of two dynamic crossovers, (i) at approximately 252 K and (ii) at approximately 181 K. Because the experiments agree with the model, we can relate the two crossovers to the presence at ambient pressure of two specific heat maxima. The first is caused by fluctuations in the HB formation, and the second, at a lower temperature, is due to the cooperative reordering of the HB network. hydrated proteins | model calculations | dielectric relaxation | water dynamics | water specific heat R ecent experiments have studied water in the first hydration shell of globular proteins (1-5). Unlike bulk water, this water does not freeze until the temperature T is well below 235 K (6), a property that may be essential to biological functioning (7). Although quasi-elastic neutron scattering investigations (1) and molecular dynamics simulations (8, 9) support the presence of a dynamic crossover at approximately 220 K, other experiments and simulations do not (2-4, 10). It has been demonstrated that the suggested crossover could be related to the anomalous behavior of water, but that it is independent of any possible liquidliquid critical point at finite T (11).Here, we show by experiments, simulations, and model calculations that the dynamic properties of the hydrogen bond (HB) network at the protein-water interface exhibit not one, but two dynamic crossovers in the one-phase region at low pressure. We show how the two crossovers are related to the thermodynamics of water. We investigate the dielectric relaxation time of water protons, due to charged defects-such as H 3 O þ -moving with a diffusive or hopping mechanism along the HB network (6, 12). These measurements are a sensitive probe for HB breaking and formation (13). We perform dielectric relaxation experiments on lysozyme powder with hydration level h ¼ 0.30 g H 2 O∕g dry protein, over a broad frequency (10 −2 s −1 -10 8 s −1 ) and temperature range (150 K ≤ T ≤ 300 K). The experimental setup and the data analysis (14-18) are described in Methods and SI Text.In the diele...
Using Wolff's cluster Monte Carlo simulations and numerical minimization within a mean field approach, we study the low temperature phase diagram of water, adopting a cell model that reproduces the known properties of water in its fluid phases. Both methods allow us to study the thermodynamic behavior of water at temperatures, where other numerical approaches -both Monte Carlo and molecular dynamics -are seriously hampered by the large increase of the correlation times. The cluster algorithm also allows us to emphasize that the liquid-liquid phase transition corresponds to the percolation transition of tetrahedrally ordered water molecules.Published by Elsevier B.V.
We demonstrate some recent progress in understanding the anomalous behavior of liquid water, by combining information provided by recent experiments and simulations on water in bulk, nanoconfined, and biological environments. We interpret evidence from recent experiments designed to test the hypothesis that liquid water may display 'polymorphism' in that it can exist in two different phases--and discuss recent work on water's transport anomalies as well as the unusual behavior of water in biological environments. Finally, we will discuss how the general concept of liquid polymorphism may prove useful in understanding anomalies in other liquids, such as silicon, silica, and carbon, as well as metallic glasses which have in common that they are characterized by two characteristic length scales in their interactions.
Here, we compare these predictions with recent quasielastic neutron scattering (QENS) experiments performed by X.-Q. Chu et al. on hydrated proteins at different values of P . We find that the experiments are consistent with these three predictions.
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