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Nowadays, although our understanding on liquid water have lots of progresses due to the development of experimental tools and computer simulation techniques, the molecular level structure of water, its heterogeneity, is still elusive. In the end of the nineteenth century, Rntgen proposed that the water is a mixture of two molecular complexes, which cannot be confirmed by experiments at that time. In the middle of the twentieth century, Bernal and his followers regarded the structure of liquid water as a random tetrahedral network, which was widely accepted by most scientists. With the development of computer science and the discovery of several amorphism, more and more attentions are paid on the mixture model of liquid water. In this paper, we firstly review some latest evidences about the multiple types of local structure in liquid water in both simulations and experiments. In all-atom simulation, the distributions of the local structure index obtained by minimizing the energy of samples are double peak at all temperatures. In experiment, the X-ray emission spectroscopy of liquid water at ambient pressure shows that there are two local structures in liquid water, one is order and ice-like, the other one is disorder and gas-like. Secondly, some results of our group on this topic are presented. We transformed the Raman spectra into the high-dimensional vectors and analyze the vectors with the principal component analysis method. The results show that all the end points of vectors are in a line in the high-dimensional space which implies that they can be obtained by linearly combining two basic points in that line. This means that the Raman spectra can be decomposed into two basic spectra. We also perform the same analysis on the distributions of tetrahedral order parameter in liquid water and obtained similar results. It is an obvious signal of the existence of multi-component in liquid water. Finally, we introduce the mixture model of liquid water which can be used to explain the thermodynamic properties of liquid water. In the mixture model, the form of the Gibbs free energy of liquid water is the same as the binary regular solution. The free energy is a function of the concentration of the disorder local structure. The anomalies of liquid water are directly caused by the change of concentration of the disorder local structure. In the low temperature and high pressure region, the mixture model has a critical point, which is consistent with the liquid-liquid phase transition theory.
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Keywords:
- liquid water /
- multiple types of local structure /
- mixture model
[1] Arunan E, Desiraju G R, Klein R A, Sadlej J, Scheiner S, Alkorta I, Clary D C, Crabtree R H, Dannenberg J J, Hobza P, Kjaergaard H G, Legon A C, Mennucci B, Nesbitt D J 2011 Pure Appl. Chem. 83 1619
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[3] Nilsson A, Pettersson L G M 2015 Nat. Commun. 6 8998
[4] Tanaka H 2012 Eur. Phys. J. E 35 1
[5] Malenkov G 2009 J. Phys. Condens. Matter 21 283101
[6] Mishima O, Calvert L D, Whalley E 1984 Nature 310 393
[7] Mishima O, Calvert L D, Whalley E 1985 Nature 314 76
[8] Handa Y P, Mishima O, Whalley E 1986 J. Chem. Phys. 84 2766
[9] Mishima O 1994 J. Chem. Phys. 100 5910
[10] Whalley E 1988 Journal of The Less Common Metals 140 361
[11] Smith J D, Cappa C D, Wilson K R, Messer B M, Cohen R C, Saykally R J 2004 Science 306 851
[12] Huang C C, Wikfeldt K T, Tokushima T, Nordlund D, Harada Y, Bergmann U, Niebuhr M, Weiss T M, Horikawa Y, Leetmaa M, Ljungberg M P, Takahashi O, Lenz A, Ojamae L, Lyubartsev A P, Shin S, Pettersson L G M, Nilsson A 2009 Proc. Natl. Acad. Sci. 106 15214
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[14] Bernal J D 1964 Proc. R. Soc. Lond. A: Math. Phys. Sci. 280 299
[15] Cuthbertson M J, Poole P H 2011 Phys. Rev. Lett. 106 115706
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[18] Shiratani E, Sasai M 1996 J. Chem. Phys. 104 7671
[19] Shiratani E, Sasai M 1998 J. Chem. Phys. 108 3264
[20] Appignanesi G A, Fris J A R, Sciortino F 2009 Eur. Phys. J. E 29 305
[21] Accordino S R, Fris J A R, Sciortino F, Appignanesi G A 2011 Eur. Phys. J. E 34 1
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[23] Wikfeldt K T 2011 Ph. D. Dissertation (Stockholm University, Faculty of Science, Department of Physics)
[24] Abascal J L F, Vega C 2005 J. Chem. Phys. 123 234505
[25] Vega C, Abascal J L F 2011 Phys. Chem. Chem. Phys. 13 19663
[26] Debenedetti P G, Stillinger F H 2001 Nature 410 259
[27] Paolantoni M, Lago N F, Albert M, Lagana A 2009 J. Phys. Chem. A 113 15100
[28] Smith J D, Cappa C D, Wilson K R, Cohen, R C, Geissler P L, Saykally R J 2005 Proc. Natl. Acad. Sci. 102 14171
[29] Vehring R, Schweiger G 1992 Appl. Spectrosc. 46 25
[30] Green J L, Lacey A R, Sceats M G 1986 J. Phys. Chem. 90 3958
[31] Tokushima T, Harada Y, Takahashi O, Senba Y, Ohashi H, Pettersson L G M, Nilsson A, Shin S 2008 Chem. Phys. Lett. 460 387
[32] Nilsson A, Huang C, Pettersson L G M 2012 J. Mol. Liq. 176 2
[33] Nilsson A, Pettersson L G M 2011 Chem. Phys. 389 1
[34] Tokushima T, Harada Y, Horikawa Y, Takahashi, O, Senba Y, Ohashi H, Pettersson L G M, Nilsson A, Shin S 2010 J. Electron Spectrosc. 177 192
[35] Abdi H, Williams L J 2010 Wiley Interdisciplinary Reviews: Computational Statistics 2 433
[36] Errington J R, Debenedetti P G 2001 Nature 409 318
[37] Ponyatovskii E G, Sinand V V, Pozdnyakova T A 1994 Jetp Lett. 60 360
[38] Ponyatovsky E G, Sinitsyn V V, Pozdnyakova T A 1998 J. Chem. Phys. 109 2413
[39] Russo J, Tanaka H 2014 Nat. Commun. 5 3556
[40] Giovambattista N 2013 Liquid Polymorphism 152 113
[41] Tanaka H 2000 Europhys. Lett. 50 340
[42] Poole P H, Sciortino F, Essmann U, Stanley H E 1992 Nature 360 324
[43] Liu D, Zhang Y, Chen C C, Mou C Y, Poole P H, Chen S H 2007 Proc. Natl. Acad. Sci. 104 9570
[44] Mallamace F, Branca C, Broccio M, Corsaro C, Mou C Y, Chen S H 2007 Proc. Natl. Acad. Sci. 104 18387
[45] Xu L, Kumar P, Buldyrev S V, Chen S H, Poole P H, Sciortino F, Stanley H E 2005 Proc. Natl. Acad. Sci. 102 16558
[46] Liu Y, Palmer J C, Panagiotopoulos A Z, Debenedetti P G 2012 J. Chem. Phys. 137 214505
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[48] Pallares G, Azouzi M E M, Gonzlez M A, Aragones J L, Abascal J L F, Valeriani C, Caupin F 2014 Proc. Natl. Acad. Sci. 111 7936
[49] Poole P H, Bowles R K, Saika-Voivod I, Sciortino F 2013 J. Chem. Phys. 138 034505
[50] Sellberg J A, Huang C, McQueen T A, Loh N D, Laksmono H, Schlesinger D, Sierra R G, Nordlund D, Hampton C Y, Starodub D, Deponte D P, Beye M, Chen C, Martin A V, Barty A, Wikfeldt K T, Weiss T M, Caronna C, Feldkamp J, Skinner L B, Seibert M M, Messerscshmidt M, Williams G J, Boutet S, Pettersson L G M, Bogan M J, Nilsson A 2014 Nature 510 381
[51] Kesselring T A, Franzese G, Buldyrev S V, Herrmann H J, Stanley H E 2012 Sci. Res. 2 474
[52] Matsumoto M, Baba A, Ohmine I 2007 J. Chem. Phys. 127 134504
[53] Sun Z R, Sun G, Chen Y X, Xu L M 2014 Sci. China: Phys. Mech. Astron. 57 810
[54] Sun G, Xu L M 2016 Sci. China: Phys. Mech. Astron. 46 057005 (in Chinese) [孙刚, 徐莉梅 2016 中国科学: 物理学 力学 天文学 46 057005]
[55] Balagurov A M, Barkalov O I, Kolesnikov A I, Mironova, G M, Ponyatovsky E G, Sinitsyn V V, Fedotov V K 1991 JETP Lett. 53 30
[56] Limmer D T, Chandler D 2011 J. Chem. Phys. 135 134503
[57] Limmer D T, Chandler D 2013 J. Chem. Phys. 138 214504
[58] Palmer J C, Martelli F, Liu Y, Car R, Panagiotopoulos A Z, Debenedetti P G 2014 Nature 510 385
[59] Liu Y, Panagiotopoulos A Z, Debenedetti P G 2009 J. Chem. Phys. 131 104508
[60] Frenkel D, Smit B 2002 Understanding Molecular Simulation: from Algorithms to Applications (2nd Ed.) (Academic Press) pp192-199
[61] Barducci A, Bussi G, Parrinello M 2008 Phys. Rev. Lett. 100 020603
[62] Duane S, Kennedy A D, Pendleton B J, Roweth D 1987 Phys. Lett. B 195 216
[63] Steinhardt P J, Nelson D R, Ronchetti M 1983 Phys. Rev. B 28 784
[64] Lechner W, Dellago C 2008 J. Chem. Phys. 129 114707
[65] Russo J, Tanaka H 2012 Sci. Res. 2 505
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[1] Arunan E, Desiraju G R, Klein R A, Sadlej J, Scheiner S, Alkorta I, Clary D C, Crabtree R H, Dannenberg J J, Hobza P, Kjaergaard H G, Legon A C, Mennucci B, Nesbitt D J 2011 Pure Appl. Chem. 83 1619
[2] Debenedetti P G 2003 J. Phys. Condens. Matter 15 R1669
[3] Nilsson A, Pettersson L G M 2015 Nat. Commun. 6 8998
[4] Tanaka H 2012 Eur. Phys. J. E 35 1
[5] Malenkov G 2009 J. Phys. Condens. Matter 21 283101
[6] Mishima O, Calvert L D, Whalley E 1984 Nature 310 393
[7] Mishima O, Calvert L D, Whalley E 1985 Nature 314 76
[8] Handa Y P, Mishima O, Whalley E 1986 J. Chem. Phys. 84 2766
[9] Mishima O 1994 J. Chem. Phys. 100 5910
[10] Whalley E 1988 Journal of The Less Common Metals 140 361
[11] Smith J D, Cappa C D, Wilson K R, Messer B M, Cohen R C, Saykally R J 2004 Science 306 851
[12] Huang C C, Wikfeldt K T, Tokushima T, Nordlund D, Harada Y, Bergmann U, Niebuhr M, Weiss T M, Horikawa Y, Leetmaa M, Ljungberg M P, Takahashi O, Lenz A, Ojamae L, Lyubartsev A P, Shin S, Pettersson L G M, Nilsson A 2009 Proc. Natl. Acad. Sci. 106 15214
[13] Rntgen W C 1891 Ann. Phys. Chem. N.F. XLV 91
[14] Bernal J D 1964 Proc. R. Soc. Lond. A: Math. Phys. Sci. 280 299
[15] Cuthbertson M J, Poole P H 2011 Phys. Rev. Lett. 106 115706
[16] Saika-Voivod I, Sciortino F, Poole P H 2000 Phys. Rev. E 63 011202
[17] Stillinger F H, Rahman A 1974 J. Chem. Phys. 60 1545
[18] Shiratani E, Sasai M 1996 J. Chem. Phys. 104 7671
[19] Shiratani E, Sasai M 1998 J. Chem. Phys. 108 3264
[20] Appignanesi G A, Fris J A R, Sciortino F 2009 Eur. Phys. J. E 29 305
[21] Accordino S R, Fris J A R, Sciortino F, Appignanesi G A 2011 Eur. Phys. J. E 34 1
[22] Wikfeldt K T, Nilsson A, Pettersson L G M 2011 Phys. Chem. Chem. Phys. 13 19918
[23] Wikfeldt K T 2011 Ph. D. Dissertation (Stockholm University, Faculty of Science, Department of Physics)
[24] Abascal J L F, Vega C 2005 J. Chem. Phys. 123 234505
[25] Vega C, Abascal J L F 2011 Phys. Chem. Chem. Phys. 13 19663
[26] Debenedetti P G, Stillinger F H 2001 Nature 410 259
[27] Paolantoni M, Lago N F, Albert M, Lagana A 2009 J. Phys. Chem. A 113 15100
[28] Smith J D, Cappa C D, Wilson K R, Cohen, R C, Geissler P L, Saykally R J 2005 Proc. Natl. Acad. Sci. 102 14171
[29] Vehring R, Schweiger G 1992 Appl. Spectrosc. 46 25
[30] Green J L, Lacey A R, Sceats M G 1986 J. Phys. Chem. 90 3958
[31] Tokushima T, Harada Y, Takahashi O, Senba Y, Ohashi H, Pettersson L G M, Nilsson A, Shin S 2008 Chem. Phys. Lett. 460 387
[32] Nilsson A, Huang C, Pettersson L G M 2012 J. Mol. Liq. 176 2
[33] Nilsson A, Pettersson L G M 2011 Chem. Phys. 389 1
[34] Tokushima T, Harada Y, Horikawa Y, Takahashi, O, Senba Y, Ohashi H, Pettersson L G M, Nilsson A, Shin S 2010 J. Electron Spectrosc. 177 192
[35] Abdi H, Williams L J 2010 Wiley Interdisciplinary Reviews: Computational Statistics 2 433
[36] Errington J R, Debenedetti P G 2001 Nature 409 318
[37] Ponyatovskii E G, Sinand V V, Pozdnyakova T A 1994 Jetp Lett. 60 360
[38] Ponyatovsky E G, Sinitsyn V V, Pozdnyakova T A 1998 J. Chem. Phys. 109 2413
[39] Russo J, Tanaka H 2014 Nat. Commun. 5 3556
[40] Giovambattista N 2013 Liquid Polymorphism 152 113
[41] Tanaka H 2000 Europhys. Lett. 50 340
[42] Poole P H, Sciortino F, Essmann U, Stanley H E 1992 Nature 360 324
[43] Liu D, Zhang Y, Chen C C, Mou C Y, Poole P H, Chen S H 2007 Proc. Natl. Acad. Sci. 104 9570
[44] Mallamace F, Branca C, Broccio M, Corsaro C, Mou C Y, Chen S H 2007 Proc. Natl. Acad. Sci. 104 18387
[45] Xu L, Kumar P, Buldyrev S V, Chen S H, Poole P H, Sciortino F, Stanley H E 2005 Proc. Natl. Acad. Sci. 102 16558
[46] Liu Y, Palmer J C, Panagiotopoulos A Z, Debenedetti P G 2012 J. Chem. Phys. 137 214505
[47] Yagasaki T, Matsumoto M, Tanaka H 2014 Phys. Rev. E 89 020301
[48] Pallares G, Azouzi M E M, Gonzlez M A, Aragones J L, Abascal J L F, Valeriani C, Caupin F 2014 Proc. Natl. Acad. Sci. 111 7936
[49] Poole P H, Bowles R K, Saika-Voivod I, Sciortino F 2013 J. Chem. Phys. 138 034505
[50] Sellberg J A, Huang C, McQueen T A, Loh N D, Laksmono H, Schlesinger D, Sierra R G, Nordlund D, Hampton C Y, Starodub D, Deponte D P, Beye M, Chen C, Martin A V, Barty A, Wikfeldt K T, Weiss T M, Caronna C, Feldkamp J, Skinner L B, Seibert M M, Messerscshmidt M, Williams G J, Boutet S, Pettersson L G M, Bogan M J, Nilsson A 2014 Nature 510 381
[51] Kesselring T A, Franzese G, Buldyrev S V, Herrmann H J, Stanley H E 2012 Sci. Res. 2 474
[52] Matsumoto M, Baba A, Ohmine I 2007 J. Chem. Phys. 127 134504
[53] Sun Z R, Sun G, Chen Y X, Xu L M 2014 Sci. China: Phys. Mech. Astron. 57 810
[54] Sun G, Xu L M 2016 Sci. China: Phys. Mech. Astron. 46 057005 (in Chinese) [孙刚, 徐莉梅 2016 中国科学: 物理学 力学 天文学 46 057005]
[55] Balagurov A M, Barkalov O I, Kolesnikov A I, Mironova, G M, Ponyatovsky E G, Sinitsyn V V, Fedotov V K 1991 JETP Lett. 53 30
[56] Limmer D T, Chandler D 2011 J. Chem. Phys. 135 134503
[57] Limmer D T, Chandler D 2013 J. Chem. Phys. 138 214504
[58] Palmer J C, Martelli F, Liu Y, Car R, Panagiotopoulos A Z, Debenedetti P G 2014 Nature 510 385
[59] Liu Y, Panagiotopoulos A Z, Debenedetti P G 2009 J. Chem. Phys. 131 104508
[60] Frenkel D, Smit B 2002 Understanding Molecular Simulation: from Algorithms to Applications (2nd Ed.) (Academic Press) pp192-199
[61] Barducci A, Bussi G, Parrinello M 2008 Phys. Rev. Lett. 100 020603
[62] Duane S, Kennedy A D, Pendleton B J, Roweth D 1987 Phys. Lett. B 195 216
[63] Steinhardt P J, Nelson D R, Ronchetti M 1983 Phys. Rev. B 28 784
[64] Lechner W, Dellago C 2008 J. Chem. Phys. 129 114707
[65] Russo J, Tanaka H 2012 Sci. Res. 2 505
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