Journal of Biological Physics

, Volume 38, Issue 1, pp 97–111 | Cite as

Effect of hydrophobic environments on the hypothesized liquid-liquid critical point of water

  • Elena G. Strekalova
  • Dario Corradini
  • Marco G. Mazza
  • Sergey V. Buldyrev
  • Paola Gallo
  • Giancarlo Franzese
  • H. Eugene Stanley
Original Paper


The complex behavior of liquid water, along with its anomalies and their crucial role in the existence of life, continue to attract the attention of researchers. The anomalous behavior of water is more pronounced at subfreezing temperatures and numerous theoretical and experimental studies are directed towards developing a coherent thermodynamic and dynamic framework for understanding supercooled water. The existence of a liquid–liquid critical point in the deep supercooled region has been related to the anomalous behavior of water. However, the experimental study of supercooled water at very low temperatures is hampered by the homogeneous nucleation of the crystal. Recently, water confined in nanoscopic structures or in solutions has attracted interest because nucleation can be delayed. These systems have a tremendous relevance also for current biological advances; e.g., supercooled water is often confined in cell membranes and acts as a solvent for biological molecules. In particular, considerable attention has been recently devoted to understanding hydrophobic interactions or the behavior of water in the presence of apolar interfaces due to their fundamental role in self-assembly of micelles, membrane formation and protein folding. This article reviews and compares two very recent computational works aimed at elucidating the changes in the thermodynamic behavior in the supercooled region and the liquid–liquid critical point phenomenon for water in contact with hydrophobic environments. The results are also compared to previous reports for water in hydrophobic environments.


Water Hydrophobic Confinement Solutions Simulations 


64.70.Ja 65.20.-w 66.10.C- 



We thank K. Stokely for discussions. D. C. and P. G. gratefully acknowledge the computational support received from CASPUR, from the INFN-GRID at Roma Tre University and from the Democritos National Simulation Center at SISSA, Trieste. G. F. thanks the Spanish MICINN grant FIS2009-10210 (co-financed FEDER). M. G. M. acknowledges support by the German Research Foundation (DFG) within the framework of the “International Graduate Research Training Group”. S. V. B. acknowledges the partial support of this research through the Dr. Bernard W. Gamson Computational Science Center at Yeshiva College. E. G. S., M. G. M. and H. E. S. acknowledge support by NSF grants CHE0908218 and CHE0911389.


  1. 1.
    Debenedetti, P.G.: Supercooled and glassy water. J. Phys., Condens. Matter 15, R1669–R1726 (2003)ADSCrossRefGoogle Scholar
  2. 2.
    Franks, F.: Water: A Matrix for Life, 2nd edn. Royal Society of Chemistry, Cambridge (2000)Google Scholar
  3. 3.
    Stanley, H.E.: A polychromatic correlated-site percolation problem with possible relevance to the unusual behavior of supercooled H2O and D2O. J. Phys. A 12, L329–L337 (1979)ADSCrossRefGoogle Scholar
  4. 4.
    Angell, C.A., Sichina, W.J., Oguni, M.: Heat capacity of water at extremes of supercooling and superheating. J. Phys. Chem. 86, 998–1002 (1982)CrossRefGoogle Scholar
  5. 5.
    Kell, G.S.: Precise representation of volume properties of water at one atmosphere. J. Chem. Eng. Data 12, 66–69 (1967)CrossRefGoogle Scholar
  6. 6.
    Poole, P.H., Sciortino, F., Essmann, U., Stanley, H.E.: Phase behaviour of metastable water. Nature 360, 324–328 (1992)ADSCrossRefGoogle Scholar
  7. 7.
    Tanaka, H.: Phase behaviors of supercooled water: reconciling a critical point of amorphous ices with spinodal instability. J. Chem. Phys. 105, 5099–5111 (1996)ADSCrossRefGoogle Scholar
  8. 8.
    Poole, P.H., Saika-Voivod, I., Sciortino, F.: Density minimum and liquid-liquid phase transition. J. Phys., Condens. Matter 17, L431–L437 (2005)ADSCrossRefGoogle Scholar
  9. 9.
    Harrington, S., Poole, P.H., Sciortino, F., Stanley, H.E.: Equation of state of supercooled SPC/E water. J. Chem. Phys. 107, 7443–7450 (1997)ADSCrossRefGoogle Scholar
  10. 10.
    Jedlovszky, P., Vallauri, R.: Liquid-vapor and liquid-liquid phase equilibria of the Brodholt-Sampoli-Vallauri polarizable water model. J. Chem. Phys. 122, 81101 (2005)CrossRefGoogle Scholar
  11. 11.
    Paschek, D., Rüppert, A., Geiger, A.: Thermodynamic and structural characterization of the transformation from a metastable low-density to a very high-density form of supercooled TIP4P-Ew model water. ChemPhysChem 9, 2737–2741 (2008)CrossRefGoogle Scholar
  12. 12.
    Liu, Y., Panagiotopoulos, A.Z., Debenedetti, P.G.: Low-temperature fluid-phase behavior of ST2 water. J. Chem. Phys. 131, 104508 (2009)ADSCrossRefGoogle Scholar
  13. 13.
    Abascal, J.L.F., Vega, C.: Widom line and the liquid-liquid critical point for the TIP4P/2005 water model. J. Chem. Phys. 133, 234502 (2010)ADSCrossRefGoogle Scholar
  14. 14.
    Franzese, G., Marqués, M.I., Stanley, H.E.: Intramolecular coupling as a mechanism for a liquid-liquid phase transition. Phys. Rev. E 67, 011103 (2003)ADSCrossRefGoogle Scholar
  15. 15.
    Chen, S.-H., Loong, C.K.: Neutron scattering investigations of proton dynamics of water and hydroxyl species in confined geometries. Nucl. Eng. Technol. 38, 201–224 (2006)Google Scholar
  16. 16.
    Liu, D., Zhang, Y., Liu, Y., Wu, J., Chen, C.-C., Mou, C.-Y., Chen, S.-H.: Density measurement of 1-D confined water by small angle neutron scattering method: pore size and hydration level dependences. J. Phys. Chem B 112, 4309–4312 (2008)CrossRefGoogle Scholar
  17. 17.
    Mallamace, F., Broccio, M., Corsaro, C., Faraone, A., Liu, L., Mou, C.-Y., Chen, S.-H.: Dynamical properties of confined supercooled water: an NMR study. J. Phys., Condens. Matter 18, S2285–S2297 (2006)ADSCrossRefGoogle Scholar
  18. 18.
    Starr, F.W., Nielsen, J.K., Stanley, H.E.: Fast and slow dynamics of hydrogen bonds in liquid water. Phys. Rev. Lett. 82, 2294–2297 (1999)ADSCrossRefGoogle Scholar
  19. 19.
    Mallamace, F., Broccio, M., Corsaro, C., Faraone, A., Majolino, D., Venuti, V., Liu, L., Mou, C.-Y., Chen, S.-H.: Evidence of the existence of the low-density liquid phase in supercooled, confined water. Proc. Natl. Acad. Sci. USA 104, 424–428 (2007)ADSCrossRefGoogle Scholar
  20. 20.
    Han, S., Kumar, P., Stanley, H.E.: Absence of a diffusion anomaly of water in the direction perpendicular to hydrophobic nanoconfining walls. Phys. Rev. E 77, 030201 (2008)ADSCrossRefGoogle Scholar
  21. 21.
    Giovambattista, N., Rossky, P.J., Debenedetti, P.: Effect of pressure on the phase behavior and structure of water confined between nanoscale hydrophobic and hydrophilic plates. Phys. Rev. E 73, 041604 (2006)ADSCrossRefGoogle Scholar
  22. 22.
    Giovambattista, N., Debenedetti, P., Rossky, P.J.: Effect of surface polarity on water contact angle and interfacial hydration structure. J. Phys. Chem. B. 111, 9581–9587 (2007)CrossRefGoogle Scholar
  23. 23.
    Majumder, M., Chopra, N., Andrews, R., Hinds, B.J.: Nanoscale hydrodynamics: enhanced flow in carbon nanotubes. Nature 438, 44 (2005)ADSCrossRefGoogle Scholar
  24. 24.
    Joseph, S., Aluru, N.R.: Pumping of confined water in carbon nanotubes by rotation-translation coupling. Phys. Rev. Lett. 101, 064502 (2008)ADSCrossRefGoogle Scholar
  25. 25.
    Strekalova, E.G., Mazza, M.G., Stanley, H.E., Franzese, G.: Large decrease of fluctuations for supercooled water in hydrophobic nanoconfinement. Phys. Rev. Lett. 106, 145701 (2011)ADSCrossRefGoogle Scholar
  26. 26.
    Gallo, P., Rovere, M.: Structural properties and liquid spinodal of water confined in a hydrophobic environment. Phys. Rev. E 76, 061202 (2007)ADSCrossRefGoogle Scholar
  27. 27.
    Gallo, P., Rovere, M., Chen, S.-H.: Dynamic crossover in supercooled confined water: understanding bulk properties through confinement. J. Phys. Chem. Lett. 1, 729–733 (2010)CrossRefGoogle Scholar
  28. 28.
    Kumar, P., Buldyrev, S.V., Starr, F.W., Giovambattista, N., Stanley, H.E.: Thermodynamics, structure, and dynamics of water confined between hydrophobic plates. Phys. Rev. E 72, 051503 (2005)ADSCrossRefGoogle Scholar
  29. 29.
    Kumar, P., Yan, Z., Xu, L., Mazza, M.G., Buldyrev, S.V., Chen, S.-H., Sastry, S., Stanley, H.E.: Glass transition in biomolecules and the liquid-liquid critical point of water. Phys. Rev. Lett. 97, 177802 (2006)ADSCrossRefGoogle Scholar
  30. 30.
    Bellissent-Funel, M.-C., Chen, S.H., Zanotti, J.-M.: Single-particle dynamics of water molecules in confined space. Phys. Rev. E 51, 4558–4569 (1995)ADSCrossRefGoogle Scholar
  31. 31.
    Swenson, J., Jansson, H., Bergman, R.: Relaxation processes in supercooled confined water and implications for protein dynamics. Phys. Rev. Lett. 96, 247802 (2006)ADSCrossRefGoogle Scholar
  32. 32.
    Mallamace, F., Broccio, M., Corsaro, C., Faraone, A., Wanderlingh, U., Liu, L., Mou, C.-Y., Chen, S. H.: The fragile-to-strong dynamic crossover transition in confined water: nuclear magnetic resonance results. J. Chem. Phys. 124, 161102 (2006)ADSCrossRefGoogle Scholar
  33. 33.
    Angell, C.A.: Insights into phases of liquid water from study of its unusual glass-forming properties. Science 319, 582–587 (2008)CrossRefGoogle Scholar
  34. 34.
    Pittia, P., Cesàro, A.: Water biophysics: how water interacts with biomolecules. Food Biophys. 6, 183–185 (2011)CrossRefGoogle Scholar
  35. 35.
    Oguni, M., Angell, C.A.: Hydrophobic and hydrophilic solute effects on the homogeneous nucleation temperature of ice from aqueous solutions. J. Phys. Chem. 87, 1848–1851 (1983)CrossRefGoogle Scholar
  36. 36.
    Corradini, D., Rovere, M., Gallo, P.: A route to explain water anomalies from results on an aqueous solution of salt. J. Chem. Phys. 132, 134508 (2010)ADSCrossRefGoogle Scholar
  37. 37.
    Corradini, D., Rovere, M., Gallo P.: Structural properties of high and low density water in a supercooled aqueous solution of salt. J. Phys. Chem. B 115, 1461–1468 (2011)CrossRefGoogle Scholar
  38. 38.
    Mishima, O.: Application of polyamorphism in water to spontaneous crystallization of emulsified LiClH 2 O. J. Chem. Phys. 123, 154506 (2005)ADSCrossRefGoogle Scholar
  39. 39.
    Mishima, O.: Phase separation in dilute LiClH 2 O solution related to the polyamorphism of liquid water. J. Chem. Phys. 126, 244507 (2007)ADSCrossRefGoogle Scholar
  40. 40.
    Huang, C., Weiss, T.M., Nordlund, D., Wikfeldt, K.T., Pettersson, L.G.M., Nilsson, A.: Increasing correlation length in bulk supercooled H 2 O, D 2 O, and NaCl solution determined from small angle x-ray scattering. J. Chem. Phys. 133, 134504 (2010)ADSCrossRefGoogle Scholar
  41. 41.
    Corradini, D., Gallo, P., Rovere, M.: Thermodynamic behavior and structural properties of an aqueous sodium chloride solution upon supercooling. J. Chem. Phys. 128, 244508 (2008)ADSCrossRefGoogle Scholar
  42. 42.
    Corradini, D., Gallo, P., Rovere, M.: Effect of concentration on the thermodynamics of sodium chloride aqueous solutions in the supercooled regime. J. Chem. Phys. 130, 154511 (2009)ADSCrossRefGoogle Scholar
  43. 43.
    Corradini, D., Gallo, P., Rovere, M.: Molecular dynamics studies on the thermodynamics of the supercooled sodium chloride aqueous solution at different concentrations. J. Phys., Condens. Matter 22, 284104 (2010)CrossRefGoogle Scholar
  44. 44.
    Corradini, D., Buldyrev, S.V., Gallo, P., Stanley, H.E.: Effect of hydrophobic solutes on the liquid-liquid critical point. Phys. Rev. E. 81 061504 (2010)ADSCrossRefGoogle Scholar
  45. 45.
    Chatterjee, S., Debenedetti, P.G.: Fluid-phase behavior of binary mixtures in which one component can have two critical points. J. Chem. Phys. 124, 154503 (2006)ADSCrossRefGoogle Scholar
  46. 46.
    Magno, A., Gallo, P.: Understanding the mechanisms of bioprotection: a comparative study of aqueous solutions of trehalose and maltose upon supercooling. J. Phys. Chem. Lett. 2, 977–982 (2011)CrossRefGoogle Scholar
  47. 47.
    Ball, P.: Water as an active constituent in cell biology. Chem. Rev. 108, 74–108 (2008)CrossRefGoogle Scholar
  48. 48.
    Ball, P.: Life’s Matrix: A Biography of Water. Farrar, Straus, and Giroux, New York (2000)Google Scholar
  49. 49.
    Granick, S., Bae S.C.: A curious antipathy for water. Science 322, 1477–1478 (2008)CrossRefGoogle Scholar
  50. 50.
    Poole, P.H., Sciortino, F., Essmann, U., Stanley, H.E.: The spinodal of liquid water. Phys. Rev. E 48, 3799–3817 (1993)ADSCrossRefGoogle Scholar
  51. 51.
    Xu, L., Kumar, P., Buldyrev, S.V., Chen, S.-H., Poole, P.H., Sciortino, F., Stanley, H.E.: Relation between the Widom line and the dynamic crossover in systems with a liquid-liquid critical point. Proc. Natl. Acad. Sci. USA 102, 16558–16562 (2005)ADSCrossRefGoogle Scholar
  52. 52.
    Xu, L., Buldyrev, S.V., Angell, C.A., Stanley, H.E.: Thermodynamics and dynamics of the two-scale spherically symmetric Jagla ramp model of anomalous liquids. Phys. Rev. E 74, 031108 (2006)ADSCrossRefGoogle Scholar
  53. 53.
    Stokely, K., Mazza, M.G., Stanley, H.E., Franzese, G.: Effect of hydrogen bond cooperativity on the behavior of water. Proc. Natl. Acad. Sci. USA 107, 1301–1306 (2010)ADSCrossRefGoogle Scholar
  54. 54.
    Urbic, T., Vlachy, V., Pizio, O., Dill, K.A.: Water-like fluid in the presence of Lennard-Jones obstacles: predictions of an associative replica Ornstein-Zernike theory. J. Mol. Liq. 112, 71 (2004)CrossRefGoogle Scholar
  55. 55.
    Zhang, Y., Liu, K.-H., Lagi, M., Liu, D., Littrell, K.C., Mou, C.-Y., Chen, S.-H.: Absence of the density minimum of supercooled water in hydrophobic confinement. J. Phys. Chem. B 113, 5007 (2009)CrossRefGoogle Scholar
  56. 56.
    Cataudella, V., Franzese, G., Nicodemi, M., Scala, A., Coniglio, A.: Percolation and cluster Monte Carlo dynamics for spin models. Phys. Rev. E 54, 175–189 (1996)ADSCrossRefGoogle Scholar
  57. 57.
    Franzese, G., Coniglio, A.: Phase transitions in the Potts spin-glass model. Phys. Rev. E 58, 2753–2759 (1998)ADSCrossRefGoogle Scholar
  58. 58.
    Wolff, U.: Collective Monte Carlo updating for spin systems. Phys. Rev. Lett. 62, 361–364 (1989)ADSCrossRefGoogle Scholar
  59. 59.
    Mazza, M.G., Stokely, K., Pagnotta, S.E., Bruni, F., Stanley, H.E., Franzese, G.: Two dynamic crossovers in protein hydration water. Proc. Natl. Acad. Sciences (2011). doi: 10.1073/pnas.1104299108 Google Scholar
  60. 60.
    Mazza, M.G., Stokely, K., Strekalova, E.G., Stanley, H.E., Franzese, G.: Cluster Monte Carlo and numerical mean field analysis for the water liquid-liquid phase transition. Comput. Phys. Commun. 180, 497–502 (2009)ADSCrossRefGoogle Scholar
  61. 61.
    Franzese, G., Bianco, V., Iskrov, S.: Water at interface with proteins. J. Food Biophys. 6, 186–198 (2011)CrossRefGoogle Scholar
  62. 62.
    Franzese, G., Stanley, H.E.: A theory for discriminating the mechanism responsible for the water density anomaly. Physica A 314, 508–513 (2002)ADSCrossRefGoogle Scholar
  63. 63.
    Franzese, G., Stanley, H.E.: Liquid-liquid critical point in a Hamiltonian model for water: analytic solution. J. Phys., Condens. Matter 14, 2201–2209 (2002)ADSCrossRefGoogle Scholar
  64. 64.
    Franzese, G., Stanley, H.E.: The Widom line of supercooled water. J. Phys., Condens. Matter 19, 205126 (2007)ADSCrossRefGoogle Scholar
  65. 65.
    Kumar, P., Franzese, G., Stanley, H.E.: Predictions of dynamic behavior under pressure for two scenarios to explain water anomalies. Phys. Rev. Lett. 100, 105701 (2008)ADSCrossRefGoogle Scholar
  66. 66.
    Kumar, P., Franzese, G., Stanley, H.E.: Dynamics and thermodynamics of water. J. Phys., Condens. Matter 20, 244114 (2008)ADSCrossRefGoogle Scholar
  67. 67.
    Franzese, G., de los Santos, F.: Dynamically slow processes in supercooled water confined between hydrophobic plates. J. Phys., Condens. Matter 21, 504107 (2009)CrossRefGoogle Scholar
  68. 68.
    Franzese, G., Hernando-Martínez, A., Kumar, P., Mazza, M.G., Stokely, K., Strekalova, E.G., de los Santos, F., Stanley, H.E.: Phase transitions and dynamics of bulk and interfacial water. J. Phys., Condens. Matter 22, 284103 (2010)CrossRefGoogle Scholar
  69. 69.
    Franzese, G., Stokely, K., Chu, X.-Q., Kumar, P., Mazza, M.G., Chen, S.-H., Stanley, H.E.: Pressure effects in supercooled water: comparison between a 2D model of water and experiments for surface water on a protein. J. Phys.: Condens. Matter 20, 494210 (2008)CrossRefGoogle Scholar
  70. 70.
    Buldyrev, S.V.: Application of discrete molecular dynamics to protein folding and aggregation. Lect. Notes Phys. 752, 97–131 (2008)ADSCrossRefGoogle Scholar
  71. 71.
    Canpolat, M., Starr, F.W., Sadr-Lahijany, M.R., Scala, A., Mishima, O., Havlin, S., Stanley, H.E.: Local structural heterogeneities in liquid water under pressure. Chem. Phys. Lett. 294, 9–12 (1998)ADSCrossRefGoogle Scholar
  72. 72.
    Sadr-Lahijany, M.R., Scala, A., Buldyrev, S.V., Stanley, H.E.: Liquid state anomalies for the Stell-Hemmer core-softened potential. Phys. Rev. Lett. 81, 4895–4898 (1998)ADSCrossRefGoogle Scholar
  73. 73.
    Xu, L., Buldyrev, S.V., Giovambattista, N., Angell, C.A., Stanley, H.E.: A monatomic system with a liquid-liquid critical point and two distinct glassy states. J. Chem. Phys. 130, 054505 (2009)ADSCrossRefGoogle Scholar
  74. 74.
    Xu, L., Ehrenberg, I., Buldyrev, S.V., Stanley, H.E.: Relationship between the liquid-liquid phase transition and dynamic behavior in the Jagla model. J. Phys.: Condens. Matter 18, S2239–S2246 (2006)ADSCrossRefGoogle Scholar
  75. 75.
    Kumar, P., Buldyrev, S.V., Sciortino, F., Zaccarelli E., Stanley, H.E.: Static and dynamic anomalies in a repulsive spherical ramp liquid: theory and simulation. Phys. Rev. E 72, 021501 (2005)MathSciNetADSCrossRefGoogle Scholar
  76. 76.
    Gibson, H.M., Wilding, N.B.: Metastable liquid-liquid coexistence and density anomalies in a core-softened fluid. Phys. Rev. E 73, 061507 (2006)ADSCrossRefGoogle Scholar
  77. 77.
    Lomba, E., Almarza, N.G., Martín, C., McBride, C.: Phase behavior of attractive and repulsive ramp fluids: integral equation and computer simulation studies. J. Chem. Phys. 126, 244510 (2007)ADSCrossRefGoogle Scholar
  78. 78.
    Franzese, G., Malescio, G., Skibinsky, A., Buldyrev, S.V., Stanley, H.E.: Generic mechanism for generating a liquid-liquid phase transition. Nature 409, 692–695 (2001)ADSCrossRefGoogle Scholar
  79. 79.
    Buldyrev, S.V., Franzese, G., Giovambattista, N., Malescio, G., Sadr-Lahijany, M.R., Scala, A., Skibinsky, A., Stanley, H.E.: Double-step potential models of fluids - Anomalies and a liquid-liquid phase transition. NATO Science Series, series II: Mathematics, Physics and Chemistry (2002)Google Scholar
  80. 80.
    Franzese, G., Malescio, G., Skibinsky, A., Buldyrev, S.V., Stanley, H.E.: Metastable liquid-liquid phase transition in a single-component system with only one crystal phase and no density anomaly. Phys. Rev. E 66, 051206 (2002)ADSCrossRefGoogle Scholar
  81. 81.
    Malescio, G., Franzese, G., Pellicane, G., Skibinsky, A., Buldyrev, S.V., Stanley, H.E.: Liquid-liquid phase transition in one-component fluids. J. Phys., Condens. Matter 14, 2193–2200 (2002)ADSCrossRefGoogle Scholar
  82. 82.
    Buldyrev, S.V., Franzese, G., Giovambattista, N., Malescio, G., Sadr-Lahijany, M.R., Scala, A., Skibinsky, A., Stanley, H.E.: Models for a liquid-liquid phase transition. Physica A 304, 23–42 (2002)ADSCrossRefGoogle Scholar
  83. 83.
    Skibinsky, A., Buldyrev, S.V., Franzese, G., Malescio, G., Stanley, H.E.: Liquid-liquid phase transitions for soft-core attractive potentials. Phys. Rev. E 69, 061206 (2004)ADSCrossRefGoogle Scholar
  84. 84.
    Malescio, G., Franzese, G., Skibinsky, A., Buldyrev, S.V., Stanley, H.E.: Liquid-liquid phase transition for an attractive isotropic potential with wide repulsive range. Phys. Rev. E 71, 061504 (2005)ADSCrossRefGoogle Scholar
  85. 85.
    Franzese, G.: Differences between discontinuous and continuous soft-core attractive potentials: the appearance of density anomaly. J. Mol. Liq. 136, 267 (2007)CrossRefGoogle Scholar
  86. 86.
    de Oliveira, A.B., Franzese, G., Netz, P.A., Barbosa, M.C.: Waterlike hierarchy of anomalies in a continuous spherical shouldered potential. J. Chem. Phys. 128, 064901 (2008)ADSCrossRefGoogle Scholar
  87. 87.
    Vilaseca, P., Franzese, G.: Softness dependence of the anomalies for the continuous shouldered well potential. J. Chem. Phys. 133, 084507 (2010)ADSCrossRefGoogle Scholar
  88. 88.
    Vilaseca, P., Franzese, G.: Isotropic soft-core potentials with two characteristic length scales and anomalous behaviour. J. Non-Cryst. Solids 357, 419–426 (2011)ADSCrossRefGoogle Scholar
  89. 89.
    Jagla, E.A.: Core-softened potentials and the anomalous properties of water. J. Chem. Phys. 111, 8980 (1999)ADSCrossRefGoogle Scholar
  90. 90.
    Jagla, E.A.: Phase behavior of a system of particles with core collapse. Phys. Rev. E 58, 1478–1486 (1998)ADSCrossRefGoogle Scholar
  91. 91.
    Yan, Z., Buldyrev, S.V., Giovambattista, N., Stanley, H.E.: Structural order for one-scale and two-scale potentials. Phys. Rev. Lett. 95, 130604 (2005)ADSCrossRefGoogle Scholar
  92. 92.
    Yan, Z., Buldyrev, S.V., Giovambattista, N., Debenedetti, P.G., Stanley, H.E.: A family of tunable spherically-symmetric potentials that span the range from hard spheres to water-like behavior. Phys. Rev. E 73, 051204 (2006)ADSCrossRefGoogle Scholar
  93. 93.
    Yan, Z., Buldyrev, S.V., Kumar, P., Giovambattista, N., Stanley, H.E.: Correspondence between phase diagrams of the TIP5P water model and a spherically symmetric repulsive ramp potential. Phys. Rev. E 77, 042201 (2008)ADSCrossRefGoogle Scholar
  94. 94.
    Xu, L., Mallamace, F., Yan, Z., Starr, F.W., Buldyrev, S.V., Stanley, H.E.: Appearance of a fractional Stokes-Einstein relation in water and a structural interpretation of its onset. Nat. Phys. 5, 565–569 (2009)CrossRefGoogle Scholar
  95. 95.
    Paschek, D.: How the liquid-liquid transition affects hydrophobic hydration in deeply supercooled water. Phys. Rev. Lett. 94, 217802 (2005)ADSCrossRefGoogle Scholar
  96. 96.
    Buldyrev, S.V., Kumar, P., Debenedetti, P.G., Rossky, P., Stanley, H.E.: Water-like solvation thermodynamics in a spherically-symmetric solvent model with two characteristic lengths. Proc. Natl. Acad. Sci. USA 104, 20177–20182 (2007)ADSCrossRefGoogle Scholar
  97. 97.
    Buldyrev, S.V., Kumar, P, Sastry, S., Stanley, H.E., Weiner, S.: Hydrophobic collapse and cold denaturation in the Jagla model of water. J. Phys., Condens. Matter 22, 284109 (2010)CrossRefGoogle Scholar
  98. 98.
    Stanley, H.E., Buldyrev, S. V., Franzese, G., Kumar, P., Mallamace, F., Mazza, M.G., Stokely, K, Xu, L.: Liquid polymorphism: water in nanoconfined and biological environments. J. Phys., Condens. Matter 22, 284101 (2010)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Elena G. Strekalova
    • 1
  • Dario Corradini
    • 1
  • Marco G. Mazza
    • 2
  • Sergey V. Buldyrev
    • 3
  • Paola Gallo
    • 4
  • Giancarlo Franzese
    • 5
  • H. Eugene Stanley
    • 1
  1. 1.Center for Polymer Studies and Department of PhysicsBoston UniversityBostonUSA
  2. 2.Stranski-Laboratorium für Physikalische und Theoretische ChemieTechnische Universität BerlinBerlinGermany
  3. 3.Department of PhysicsYeshiva UniversityNew YorkUSA
  4. 4.Dipartimento di FisicaUniversità Roma TreRomaItaly
  5. 5.Departament de Fisica FonamentalUniversitat de BarcelonaBarcelonaSpain

Personalised recommendations