The aim of this paper is to discuss the relationship between the dynamics and thermodynamics of water in the supercooled region. Reviewed case studies comprehend bulk water simulated with the SPC/E, TIP4P and TIP4P/2005 potentials, water at protein interfaces, and water in solution with electrolytes. Upon supercooling, the fragile to strong crossover in the-relaxation of water is found to occur when the Widom line emanating from the liquid-liquid critical point is crossed. This appears to be a general characteristic of supercooled water, not depending on the applied interaction potential and/or different local environments.
P. Gallo, K. Amann-Winkel, C. A. Angell, M. A. Anisimov, F. Caupin, C. Chakravarty, E. Lascaris, T. Loerting, A. Z. Panagiotopoulos, J. Russo, J. A. Sellberg, H. E. Stanley, H. Tanaka, C. Vega, L. Xu, and G. M. P. Lars, Water: A tale of two liquids, Chem. Rev. 116(13), 7463 (2016) https://doi.org/10.1021/acs.chemrev.5b00750
C. A. Angell, R. D. Bressel, M. Hemmati, E. J. Sare, and J. C. Tucker, Water and its anomalies in perspective: Tetrahedral liquids with and without liquid-liquid phase transitions, Phys. Chem. Chem. Phys. 2(8), 1559 (2000) https://doi.org/10.1039/b000206m
5
P. G. Debenedetti, Metastable Liquids: Concepts and Principles, Princeton: Princeton University Press, 1996
6
A. Sakai, T. Matsumoto, D. Hirai, and T. Niino, Newly developed encapsulation-dehydration protocol for plantcryopreservation, Cryo Lett. 21(1), 53 (1999)
C. A. Angell, J. Shuppert, and J. C. Tucker, Anomalous properties of supercooled water. Heat capacity, expansivity, and proton magnetic resonance chemical shift from 0 to －38%, J. Phys. Chem. 77(26), 3092 (1973) https://doi.org/10.1021/j100644a014
11
R. J. Speedy and C. A. Angell, Isothermal compressibility of supercooled water and evidence for a thermodynamic singularity at －45 ◦C, J. Chem. Phys. 65(3), 851 (1976) https://doi.org/10.1063/1.433153
12
O. Mishima and H. E. Stanley, The relationship between liquid, supercooled and glassy water, Nature 396(6709), 329 (1998) https://doi.org/10.1038/24540
13
P. H. Poole, F. Sciortino, U. Essmann, and H. E. Stanley, Phase behaviour of metastable water, Nature 360(6402), 324 (1992) https://doi.org/10.1038/360324a0
14
K. Winkel, M. S. Elsaesser, E. Mayer, and T. Loerting, Water polyamorphism: Reversibility and (dis) continuity, J. Chem. Phys. 128(4), 044510 (2008) https://doi.org/10.1063/1.2830029
15
O. Mishima and H. E. Stanley, Decompression-induced melting of ice IV and the liquid-liquid transition in water, Nature 392(6672), 164 (1998) https://doi.org/10.1038/32386
16
O. Mishima, L. D. Calvert, and E. Whalley, An apparently first-order transition between two amorphous phases of ice induced by pressure, Nature 314(6006), 76 (1985) https://doi.org/10.1038/314076a0
17
K. Winkel, E. Mayer, and T. Loerting, Equilibrated high-density amorphous ice and its first-order transition to the low-density form, J. Phys. Chem. B 115(48), 14141 (2011) https://doi.org/10.1021/jp203985w
18
C. U. Kim, B. Barstow, M. V. Tate, and S. M. Gruner, Evidence for liquid water during the high-density to lowdensity amorphous ice transition, Proc. Natl. Acad. Sci. USA 106(12), 4596 (2009) https://doi.org/10.1073/pnas.0812481106
L. Xu, P. Kumar, S. V. Buldyrev, S. H. Chen, P. H. Poole, F. Sciortino, and H. E. Stanley, Relation between the Widom line and the dynamic crossover in systems with a liquid-liquid phase transition, Proc. Natl. Acad. Sci. USA 102(46), 16558 (2005) https://doi.org/10.1073/pnas.0507870102
21
D. Corradini, M. Rovere, and P. Gallo, A route to explain water anomalies from results on an aqueous solution of salt, J. Chem. Phys. 132(13), 134508 (2010) https://doi.org/10.1063/1.3376776
22
J. L. F. Abascal and C. Vega, Widom line and the liquidliquid critical point for the TIP4P/2005 water model, J. Chem. Phys. 133(23), 234502 (2010) https://doi.org/10.1063/1.3506860
23
P. Gallo, F. Sciortino, P. Tartaglia, and S. H. Chen, Slow dynamics of water molecules in supercooled states, Phys. Rev. Lett. 76(15), 2730 (1996) https://doi.org/10.1103/PhysRevLett.76.2730
24
F. Sciortino, P. Gallo, P. Tartaglia, and S. H. Chen, Supercooled water and the kinetic glass transition, Phys. Rev. E 54(6), 6331 (1996) https://doi.org/10.1103/PhysRevE.54.6331
W. Götze, Complex Dynamics of Glass-Forming Liquids: A Mode-Coupling Theory, Oxford: Oxford University Press, 2009
27
P. Gallo and M. Rovere, Mode coupling and fragile to strong transition in supercooled TIP4P water,J. Chem. Phys. 137(16), 164503 (2012) https://doi.org/10.1063/1.4759262
28
P. Gallo, D. Corradini, and M. Rovere, Fragile to strong crossover at the Widom line in supercooled aqueous solutions of NaCl, J. Chem. Phys. 139(20), 204503 (2013) https://doi.org/10.1063/1.4832382
29
P. Gallo, M. Rovere, and E. Spohr, Supercooled confined water and the mode coupling crossover temperature, Phys. Rev. Lett. 85(20), 4317 (2000) https://doi.org/10.1103/PhysRevLett.85.4317
30
P. Gallo, M. Rovere, and E. Spohr, Glass transition and layering effects in confined water: A computer simulation study, J. Chem. Phys. 113(24), 11324 (2000) https://doi.org/10.1063/1.1328073
31
P. Gallo, M. Rovere, and S. H. Chen, Dynamic crossover in supercooled confined water: Understanding bulk properties through confinement, J. Phys. Chem. Lett. 1(4), 729 (2010) https://doi.org/10.1021/jz9003125
32
P. Gallo, M. Rovere, and S. H. Chen, Water confined in MCM-41: A mode coupling theory analysis, J. Phys.: Condens. Matter 24(6), 064109 (2012) https://doi.org/10.1088/0953-8984/24/6/064109
33
M. De Marzio, G. Camisasca, M. Rovere, and P. Gallo, Mode coupling theory and fragile to strong transition in supercooled TIP4P/2005 water, J. Chem. Phys. 144(7), 074503 (2016) https://doi.org/10.1063/1.4941946
34
A. Dehaoui, B. Issenmann, and F. Caupin, Viscosity of deeply supercooled water and its coupling to molecular diffusion, Proc. Natl. Acad. Sci. USA 112(39), 12020 (2015) https://doi.org/10.1073/pnas.1508996112
35
R. Torre, P. Bartolini, and R. Righini, Structural relaxation in supercooled water by time-resolved spectroscopy, Nature 428(6980), 296 (2004) https://doi.org/10.1038/nature02409
36
F. W. Starr, F. Sciortino, and H. E. Stanley, Dynamics of simulated water under pressure, Phys. Rev. E 60(6), 6757 (1999) https://doi.org/10.1103/PhysRevE.60.6757
37
A. Faraone, L. Liu, C. Y. Mou, C. W. Yen, and S. H. Chen, Fragile-to- strong liquid transition in deeply supercooled confined water, J. Chem. Phys. 121(22), 10843 (2004) https://doi.org/10.1063/1.1832595
38
L. Liu, S. H. Chen, A. Faraone, C. W. Yen, and C. Y. Mou, Pressure dependence of fragile-to-strong transition and a possible second critical point in supercooled confined water, Phys. Rev. Lett. 95(11), 117802 (2005) https://doi.org/10.1103/PhysRevLett.95.117802
39
F. Mallamace, M. Broccio, C. Corsaro, A. Faraone, U. Wanderlingh, L. Liu, C. Y. Mou, and S. H. Chen, The fragile-to-strong dynamic crossover transition in confined water: nuclear magnetic resonance results, J. Chem. Phys. 124(16), 161102 (2006) https://doi.org/10.1063/1.2193159
40
Y. Zhang, M. Lagi, E. Fratini, P. Baglioni, E. Mamontov, and S. H. Chen, Dynamic susceptibility of supercooled water and its relation to the dynamic crossover phenomenon, Phys. Rev. E 79(4), 040201 (2009) https://doi.org/10.1103/PhysRevE.79.040201
41
L. Liu, S. H. Chen, A. Faraone, C.W. Yen, C. Y. Mou, A. I. Kolesnikov, E. Mamontov, and J. Leao, Quasielastic and inelastic neutron scattering investigation of fragile-to-strong crossover in deeply supercooled water confined in nanoporous silica matrices, J. Phys.: Condens. Matter 18(36), S2261 (2006) https://doi.org/10.1088/0953-8984/18/36/S03
42
Z. Wang, P. Le, K. Ito, J. B. Leão, M. Tyagi, and S. H. Chen, Dynamic crossover in deeply cooled water confined in mcm-41 at 4 kbar and its relation to the liquidliquid transition hypothesis, J. Chem. Phys. 143(11), 114508 (2015) https://doi.org/10.1063/1.4930855
43
Y. Xu, N. G. Petrik, R. S. Smith, B. D. Kay, and G. A. Kimmel, Growth rate of crystalline ice and the diffusivity of supercooled water from 126 to 262 K, Proc. Natl. Acad. Sci. USA 113(52), 14921 (2016) https://doi.org/10.1073/pnas.1611395114
44
J. M. Zanotti, M. C. Bellissent-Funel, and S. H. Chen, Relaxational dynamics of supercooled water in porous glass, Phys. Rev. E 59(3), 3084 (1999) https://doi.org/10.1103/PhysRevE.59.3084
45
P. Gallo, M. Rovere, and S. H. Chen, Anomalous dynamics of water confined in MCM-41 at different hydrations, J. Phys.: Condens. Matter 22(28), 284102 (2010) https://doi.org/10.1088/0953-8984/22/28/284102
46
W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, and M. L. Klein, Comparison of simple potential functions for simulating liquid water, J. Chem. Phys. 79(2), 926 (1983) https://doi.org/10.1063/1.445869
47
J. L. F. Abascal and C. Vega, A general purpose model for the condensed phases of water: TIP4P/2005, J. Chem. Phys. 123(23), 234505 (2005) https://doi.org/10.1063/1.2121687
48
G. Camisasca, M. De Marzio, D. Corradini, and P. Gallo, Two structural relaxations in protein hydration water and their dynamic crossovers, J. Chem. Phys. 145(4), 044503 (2016) https://doi.org/10.1063/1.4959286
49
J. C. Herman,Berendsen, J. R. Grigera, and T. P. Straatsma. The missing term in effective pair potentials, J. Phys. Chem. 91(24), 6269 (1987) https://doi.org/10.1021/j100308a038
50
A. D. MacKerell, D. Bashford, M. Bellott, R. L. Dunbrack, J. D. Evanseck, M. J. Field, S. Fischer, J. Gao, H. Guo, S. Ha, D. Joseph-McCarthy, L. Kuchnir, K. Kuczera, F. T. Lau, C. Mattos, S. Michnick, T. Ngo, D. T. Nguyen, B. Prodhom, W. E. Reiher, B. Roux, M. Schlenkrich, J. C. Smith, R. Stote, J. Straub, M. Watanabe, J. Wiórkiewicz-Kuczera, D. Yin, and M. Karplus, All-atom empirical potential for molecular modeling and dynamics studies of proteins, J. Phys. Chem. B 102(18), 3586 (1998) https://doi.org/10.1021/jp973084f
51
A. D. MacKerell, M. Feig, and C. L. Brooks, Extending the treatment of backbone energetics in protein force fields: limitations of gas-phase quantum mechanics in reproducing protein conformational distributions in molecular dynamics simulations, J. Comput. Chem. 25(11), 1400 (2004) https://doi.org/10.1002/jcc.20065
52
A. Scala, F. W. Starr, E. La Nave, H. E. Stanley, and F. Sciortino, Free energy surface of supercooled water, Phys. Rev. E 62(6), 8016 (2000) https://doi.org/10.1103/PhysRevE.62.8016
53
D. Corradini and P. Gallo, Liquid-liquid coexistence in nacl aqueous solutions: a simulation study of concentration effects, J. Phys. Chem. B 115, 1461 (2011) https://doi.org/10.1021/jp1101237
54
D. Corradini, M. Rovere, and P. Gallo, Structural properties of high and low density water in a supercooled aqueous solution of salt, J. Phys. Chem. B 115(6), 1461 (2011) https://doi.org/10.1021/jp1101237
55
C. Vega, J. L. F. Abascal, M. M. Conde, and J. L. Aragones, What ice can teach us about water interactions: A critical comparison of the performance of different water models, Faraday Discuss. 141, 251 (2009) https://doi.org/10.1039/B805531A
56
K. P. Jensen and W. L. Jorgensen, Halide, ammonium, and alkali metal ion parameters for modeling aqueous solutions, J. Chem. Theory Comput. 2(6), 1499 (2006) https://doi.org/10.1021/ct600252r
57
A. Magno and P. Gallo, Understanding the Mechanisms of Bioprotection: A Comparative Study of Aqueous Solutions of Trehalose and Maltose upon Supercooling, J. Phys. Chem. Lett. 2(9), 977 (2011) https://doi.org/10.1021/jz200256q
58
D. Corradini, E. G. Strekalova, H. E. Stanley, and P. Gallo, Microscopic mechanism of protein cryopreservation in an aqueous solution with trehalose, Sci. Rep. 3(1), 1218 (2013) https://doi.org/10.1038/srep01218
59
P. Kumar, Z. Yan, Limei Xu, M. G. Mazza, S. V. Buldyrev, S. H. Chen, S. Sastry, and H. E. Stanley, Glass transition in biomolecules and the liquid-liquid critical point of water, Phys. Rev. Lett. 97(17), 177802 (2006) https://doi.org/10.1103/PhysRevLett.97.177802
60
S. H. Chen, L. Liu, E. Fratini, P. Baglioni, A. Faraone, E. Mamontov, and M. Fomina, Observation of fragileto- strong dynamic crossover in protein hydration water, Proc. Natl. Acad. Sci. USA 103(24), 9012 (2006) https://doi.org/10.1073/pnas.0602474103
