The Widom line of supercooled water

Franzese, Giancarlo; Stanley, H. Eugene

doi:10.1088/0953-8984/19/20/205126

Cited by 161 publications

(229 citation statements)

References 79 publications

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“…This model is studied using both MF analysis and Monte Carlo (MC) simulations (25,(34)(35)(36)(37). Details of the MF and MC techniques are available elsewhere (25,38).…”

Section: Cooperative Cell Model Of Watermentioning

confidence: 99%

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Effect of hydrogen bond cooperativity on the behavior of water

Stokely

Mazza

Stanley

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

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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...

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“…This model is studied using both MF analysis and Monte Carlo (MC) simulations (25,(34)(35)(36)(37). Details of the MF and MC techniques are available elsewhere (25,38).…”

Section: Cooperative Cell Model Of Watermentioning

confidence: 99%

“…Details of the MF and MC techniques are available elsewhere (25,38). In the following we adoptJ ≡ J∕ϵ,J σ ≡ J σ ∕ϵ, and v HB ¼ v 0 ∕2.…”

Section: Cooperative Cell Model Of Watermentioning

confidence: 99%

Effect of hydrogen bond cooperativity on the behavior of water

Stokely

Mazza

Stanley

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

Self Cite

256

250

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“…Our results point to the coincidence of the extrema of both solubility and density, in agreement with theories based on the cavity model for simple hard spheres. [7][8][9] Even though there are a number of two and three dimensional lattice models that would in principle exhibit the anomalies present in water, 6,16,[19][20][21] here water is represented by the associating lattice gas (ALG) (Refs. [22][23][24][25][26][27][28]) that has already shown the density and diffusion anomalies described above.…”

Section: Introductionmentioning

confidence: 99%

Structure and anomalous solubility for hard spheres in an associating lattice gas model

Szortyka

Girardi

Henriques

et al. 2012

The Journal of Chemical Physics

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In this paper we investigate the solubility of a hard-sphere gas in a solvent modeled as an associating lattice gas. The solution phase diagram for solute at 5% is compared with the phase diagram of the original solute free model. Model properties are investigated both through Monte Carlo simulations and a cluster approximation. The model solubility is computed via simulations and is shown to exhibit a minimum as a function of temperature. The line of minimum solubility (TmS) coincides with the line of maximum density (TMD) for different solvent chemical potentials, in accordance with the literature on continuous realistic models and on the "cavity" picture.

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“…The shape of the curve is consistent with results of Sastry 42 and Franzese. 77 In our theory we have all molecules forming hydrogen bonds at low temperatures while at high temperature there is almost no hydrogen bond. Figure 9͑a͒ shows the model populations of the strong hydrogen-bonding state, weak hydrogen-bonding state, and the state of no hydrogen bonds versus temperature, indicating the melting out of strong hydrogen bonding with temperature and the melting out of weak hydrogen-bonding interactions at higher temperatures.…”

Section: Resultsmentioning

confidence: 99%

A statistical mechanical theory for a two-dimensional model of water

Urbič

Dill²

2010

The Journal of Chemical Physics

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We develop a statistical mechanical model for the thermal and volumetric properties of waterlike fluids. Each water molecule is a two-dimensional disk with three hydrogen-bonding arms. Each water interacts with neighboring waters through a van der Waals interaction and an orientation-dependent hydrogen-bonding interaction. This model, which is largely analytical, is a variant of the Truskett and Dill ͑TD͒ treatment of the "Mercedes-Benz" ͑MB͒ model. The present model gives better predictions than TD for hydrogen-bond populations in liquid water by distinguishing strong cooperative hydrogen bonds from weaker ones. We explore properties versus temperature T and pressure p. We find that the volumetric and thermal properties follow the same trends with T as real water and are in good general agreement with Monte Carlo simulations of MB water, including the density anomaly, the minimum in the isothermal compressibility, and the decreased number of hydrogen bonds for increasing temperature. The model reproduces that pressure squeezes out water's heat capacity and leads to a negative thermal expansion coefficient at low temperatures. In terms of water structuring, the variance in hydrogen-bonding angles increases with both T and p, while the variance in water density increases with T but decreases with p. Hydrogen bonding is an energy storage mechanism that leads to water's large heat capacity ͑for its size͒ and to the fragility in its cagelike structures, which are easily melted by temperature and pressure to a more van der Waals-like liquid state.

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The Widom line of supercooled water

Cited by 161 publications

References 79 publications

Effect of hydrogen bond cooperativity on the behavior of water

Effect of hydrogen bond cooperativity on the behavior of water

Structure and anomalous solubility for hard spheres in an associating lattice gas model

A statistical mechanical theory for a two-dimensional model of water

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