Cluster Monte Carlo and numerical mean field analysis for the water liquid–liquid phase transition

Mazza, Marco G.; Stokely, Kevin; Strekalova, Elena G.; Stanley, H. Eugene; Franzese, Giancarlo

doi:10.1016/j.cpc.2009.01.018

Cited by 39 publications

(72 citation statements)

References 24 publications

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“…To test the validity of our MF calculations, we perform MC simulations in the NPT ensemble (38). To this end, (i) we consider that the total volume is V ≡ V MC þ N HB v HB , where V MC ⩾Nv 0 is a dynamical continuous variable;…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

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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263

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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: Resultsmentioning

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

263

250

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“…[34][35][36][37] Many more computer simulations investigating the phenomenology of the liquid-liquid critical point (LLCP) have been performed since then. [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55] Detailed studies using ST2-RF have been made by Poole et al 56 using molecular dynamics, while Liu et al 57,58 simulated ST2 with Ewald summation (ST2-Ew) for the electrostatic long-range potential using Monte Carlo. Also in other water models the LLPT and its LLCP are believed to be found, for example, by Yamada et al 59 in the TIP5P model, by Paschek et al 60 in the TIP4P-Ew model, and in TIP4P/2005 by Abascal and Vega.…”

Section: Introductionmentioning

confidence: 99%

Finite-size scaling investigation of the liquid-liquid critical point in ST2 water and its stability with respect to crystallization

Kesselring

Lascaris

Franzese

et al. 2013

The Journal of Chemical Physics

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The liquid-liquid critical point scenario of water hypothesizes the existence of two metastable liquid phases-low-density liquid (LDL) and high-density liquid (HDL)-deep within the supercooled region. The hypothesis originates from computer simulations of the ST2 water model, but the stability of the LDL phase with respect to the crystal is still being debated. We simulate supercooled ST2 water at constant pressure, constant temperature, and constant number of molecules N for N ≤ 729 and times up to 1 μs. We observe clear differences between the two liquids, both structural and dynamical. Using several methods, including finite-size scaling, we confirm the presence of a liquid-liquid phase transition ending in a critical point. We find that the LDL is stable with respect to the crystal in 98% of our runs (we perform 372 runs for LDL or LDL-like states), and in 100% of our runs for the two largest system sizes (N = 512 and 729, for which we perform 136 runs for LDL or LDL-like states). In all these runs, tiny crystallites grow and then melt within 1 μs. Only for N ≤ 343 we observe six events (over 236 runs for LDL or LDL-like states) of spontaneous crystallization after crystallites reach an estimated critical size of about 70 ± 10 molecules. © 2013 AIP Publishing LLC. [http://dx

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“…In our simulations we update the variables ij using the Wolff cluster algorithm [73]. The algorithm is based on an exact mapping of the model studied here to a percolation problem, following the mapping rules described in [82,83].…”

Section: Monte Carlo Simulationsmentioning

confidence: 99%

“…where V 0 Nv 0 is a continuous variable that changes with pressure in such a way that V follows the water equation of state [73]. Note that only the term V 0 of the fluctuating volume is considered for the calculation of distances r appearing in equation (2) for the isotropic interaction U(r), because the HB formation does not imply an increase of molecular distances, but only an increase of the local tetrahedral structure with the exclusion of interstitial water molecules between the first and the second shell.…”

Section: Coarse-grained Model Of Water Monolayermentioning

confidence: 99%

Hydrophobic nanoconfinement suppresses fluctuations in supercooled water

Strekalova¹,

Mazza²,

Stanley³

et al. 2012

J. Phys.: Condens. Matter

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We perform very efficient Monte Carlo simulations to study the phase diagram of a water monolayer confined in a fixed disordered matrix of hydrophobic nanoparticles between two hydrophobic plates. We consider different hydrophobic nanoparticle concentrations c. We adopt a coarse-grained model of water that, for c = 0, displays a first-order liquid-liquid phase transition (LLPT) line with negative slope in the pressure-temperature (P-T) plane, ending in a liquid-liquid critical point at about 174 K and 0.13 GPa. We show that upon increase of c the liquid-gas spinodal and the temperature of the maximum density line are shifted with respect to the c = 0 case. We also find dramatic changes in the region around the LLPT. In particular, we observe a substantial (more than 90%) decrease of isothermal compressibility, thermal expansion coefficient and constant-pressure specific heat upon increasing c, consistent with recent experiments. Moreover, we find that a hydrophobic nanoparticle concentration as small as c = 2.4% is enough to destroy the LLPT for P 0.16 GPa. The fluctuations of volume apparently diverge at P ⇡ 0.16 GPa, suggesting that the LLPT line ends in an LL critical point at 0.16 GPa. Therefore, nanoconfinement reduces the range of P-T where the LLPT is observable. By increasing the hydrophobic nanoparticle concentration c, the LLPT becomes weaker and its P-T range smaller. The model allows us to explain these phenomena in terms of a proliferation of interfaces among domains with different local order, promoted by the hydrophobic effect of the water-hydrophobic-nanoparticle interfaces.

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Cluster Monte Carlo and numerical mean field analysis for the water liquid–liquid phase transition

Cited by 39 publications

References 24 publications

Effect of hydrogen bond cooperativity on the behavior of water

Effect of hydrogen bond cooperativity on the behavior of water

Finite-size scaling investigation of the liquid-liquid critical point in ST2 water and its stability with respect to crystallization

Hydrophobic nanoconfinement suppresses fluctuations in supercooled water

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