Liquid-liquid critical point in a Hamiltonian model for water: analytic solution

Franzese, Giancarlo; Stanley, H. Eugene

doi:10.1088/0953-8984/14/9/309

Cited by 99 publications

(117 citation statements)

References 56 publications

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“…We analyze a microscopic model of water in which the fluid is divided into N cells with nearest neighbor (NN) interactions (19). The division is such that each cell is in contact with four NNs mimicking the first shell of liquid water (20).…”

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.

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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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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

263

250

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“…For water observation is precluded by a zone of homogeneous nucleation that surrounds it in temperature-pressure or T-P configurational space (Debenedetti 1997). The anomalous rise in isothermal compressibility above this zone but in the vicinity of T C P C (Speedy & Angell 1976;Franzese & Stanley 2002;Fuentevilla & Anisimov 2006), the switch in Raman frequencies and change in specimen volume during annealing (Mishima & Suzuki 2002) below, however, point to critical liquid-liquid fluctuations spreading out extensively in configurational space in common with other critical phenomena (Stanley 1971). In particular, the power laws (Stanley 1971), where κ T C and ξ T C are the critical isothermal compressibility (or susceptibility) and the time-averaged fluctuation correlation length respectively, and the exponents γ and ν are linked by γ ≈ 2ν ≈ 1.2 (Stanley 1971).…”

Section: Critical Phenomena In Liquidsmentioning

confidence: 99%

Polyamorphism and the universal liquid–liquid critical point in the supercooled state

Greaves

2010

DLS Proc.

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The physics of critical phenomena is well established in systems as diverse as molecular fluids, crystalline alloys and magnetic materials. As the critical point is approached, the susceptibility increases anomalously and fluctuations give rise to dramatic opalescence. Evidence has recently emerged for the existence of a second critical point in the liquid state at supercooled temperatures, below which polyamorphic phases coexist differing in density but sharing the same composition. Whilst much attention has been paid to supercooled water, polyamorphic phases have been observed in many elemental and oxide liquids potentially offering routes to low-entropy glasses. Our recent direct observation of a polyamorphic phase transition in levitated molten yttria-alumina offers the first opportunity to study the associated critical point in a real supercooled system. In situ small-angle X-ray scattering records sharp rises in the average correlation length of density fluctuations and in the compressibility as the transition is approached. Both increases approximate to the universal power-law relations predicted by the three-dimensional Ising model in common with all critical point phenomena. The observation brings the second critical point predicted in liquids into line with other critical phenomena.

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“…These models originate from the desire to construct a simple two-body isotropic potential capable of the density [2][3][4] and diffusion [4][5][6] anomalies present in water. Another motivation for these studies is the acknowledged possibility that some single component systems display coexistence between two different liquid phases [7][8][9][10][11][12]. The use of two length scales potentials seems to be an interesting tool for finding the connection between the presence of thermodynamic and dynamic anomalies and the possibility of the presence of two liquid phase.…”

Section: Introductionmentioning

confidence: 99%

Critical points, phase transitions and water-like anomalies for an isotropic two length scale potential with increasing attractive well

Pinheiro

Furlan

Krott

et al. 2017

Physica A: Statistical Mechanics and its Applications

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Molecular Dynamic and Monte Carlo studies are performed in a family of core-softened (CS) potential, composed by two length scales: a repulsive shoulder at short distances and the another a variable scale, that can be repulsive or strongly attractive depending on the parameters used.The density, diffusion and structural anomalous regions in the pressure versus temperature phase diagram shrink in pressure as the system becomes more attractive. The liquid-liquid transition appears as a consequence of the non monotonic behavior of the density versus pressure isotherms with the increase of the attraction well. We found that the liquid-gas phase transition is Ising-like for all the CS potentials and its critical temperature increases with the increase of the attraction. No Ising-like behavior for the liquid-liquid phase transition was detected in the Monte Carlo simulations what might be due to the presence of stable solid phases.

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Liquid-liquid critical point in a Hamiltonian model for water: analytic solution

Cited by 99 publications

References 56 publications

Effect of hydrogen bond cooperativity on the behavior of water

Effect of hydrogen bond cooperativity on the behavior of water

Polyamorphism and the universal liquid–liquid critical point in the supercooled state

Critical points, phase transitions and water-like anomalies for an isotropic two length scale potential with increasing attractive well

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