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There are a number of liquids that have a density maximum in the liquid phase. The most celebrated is that of [[water]], which was first reported in 1792<ref>[http://dx.doi.org/10.1098/rstl.1792.0026 Charles Blagden and George Gilpin "Supplementary Report on the Best Method of Proportioning the Excise upon Spirituous Liquors", Philosophical Transactions of the Royal Society of London '''82''' pp. 425-455 (1792)]</ref>. However, liquid [[helium]] 4 also has a maximum at 2.18 K (Ref. ??), liquid [[gallium]] at ??K (Ref. ??), [[silica]] at ??K (Ref. ??), [[tellurium]] (Ref. <ref>[http://dx.doi.org/10.1103/PhysRevB.65.014105 Nobumasa Funamori and Kazuhiko Tsuji "Structural transformation of liquid tellurium at high pressures and temperatures", Physical Review B '''65''' 014105 (2001)]</ref>), and [[germanium]] at ?? (Ref. ??). [[Bismuth]]  appears not to have a density maximum within the liquid phase, however the "low temperature" liquid does appear to be denser than the "high temperature" solid (Ref. <ref>[http://dx.doi.org/10.1007/s10740-005-0075-7 S. V. Stankus, R. A. Khairulin, A. G. Mozgovoi, V. V. Roshchupkin and M. A. Pokrasin "An Experimental Investigation of the Density of Bismuth in the Condensed State in a Wide Temperature Range", High Temperature '''43''' pp. 368-378 (2005)]</ref>),
{{Stub-general}}
There are a number of liquids that have a density maximum in the liquid phase. The most celebrated is that of [[water]]. However, liquid [[helium]] 4 also has a maximum at 2.18 K (Ref. ??), liquid [[gallium]] at ??K (Ref. ??), [[silica]] at ??K (Ref. ??), and [[tellurium]] at ??K (Ref. ??).
==Historical papers==
Water:
#[http://dx.doi.org/10.1098/rstl.1792.0026 Charles Blagden and George Gilpin "Supplementary Report on the Best Method of Proportioning the Excise upon Spirituous Liquors", Philosophical Transactions of the Royal Society of London '''82''' pp. 425-455 (1792)]
==Water==
==Water==
:{| border="1"
:{| border="1"
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| System || model || <math>T_{\mathrm {TMD}}</math> (K) || density at <math>T=T_{\mathrm {TMD}}</math> (Kg/m<sup>3</sup>) || Reference
| System || model || <math>T_{\mathrm {TMD}}</math> (K) || density at <math>T=T_{\mathrm {TMD}}</math> (Kg/m<sup>3</sup>) || Reference
|-   
|-   
| H<sub>2</sub>O || experimental  ||  277.134 || 999.972 ||<ref name="Franks">[http://dx.doi.org/10.1021/je60032a018 G. S. Kell "Precise representation of volume properties of water at one atmosphere", Journal of Chemical & Engineering Data  '''12''' pp. 66-69 (1967)] </ref>
| H<sub>2</sub>O || experimental  ||  277.134 || 999.972 ||Ref. 1
|-   
|-   
| D<sub>2</sub>O || experimental  ||  284.335 || 1106.00 || <ref>[http://dx.doi.org/10.1063/1.555661 P. G. Hill, R. D. Chris MacMillan, and V. Lee "A Fundamental Equation of State for Heavy Water", Journal of Physical and Chemical Reference Data '''11''' pp. 1-14 (1982)]</ref>
| D<sub>2</sub>O || experimental  ||  284.335 || 1106.00 || Ref. 1
|-   
|-   
| T<sub>2</sub>O || experimental  ||  286.553 || 1215.02 || <ref>[http://dx.doi.org/10.1021/j100783a024 Maxwell Goldblatt "The Density of Liquid T2O", Journal of Physical Chemistry '''68''' pp. 147-151 (1964)]</ref>
| T<sub>2</sub>O || experimental  ||  286.553 || 1215.01 ||Ref. 1
|-   
|-   
| H<sub>2</sub>O || [[ST2]]  ||  300  || || <ref>[http://dx.doi.org/10.1063/1.1681229  Frank H. Stillinger and Aneesur Rahman "Improved simulation of liquid water by molecular dynamics", Journal of Chemical Physics '''60''' pp. 1545-1557 (1974)]</ref>
| H<sub>2</sub>O || [[ST2]]  ||  300  || ||Ref. 2
|-   
|-   
| H<sub>2</sub>O || [[TIPS2]]  ||  298 <math>\pm</math> 25 || || <ref>[http://dx.doi.org/10.1063/1.444325 William L. Jorgensen "Revised TIPS for simulations of liquid water and aqueous solutions", Journal of Chemical Physics '''77''' pp. 4156- (1982)]</ref>
| H<sub>2</sub>O || [[TIPS2]]  ||  298 <math>\pm</math> 25 || || Ref. 3
|-   
|-   
| H<sub>2</sub>O || [[SPC]]  ||  228 || 1008 || <ref name="vegaAbascal"> [http://dx.doi.org/10.1063/1.2056539 C. Vega and J. L. F. Abascal "Relation between the melting temperature and the temperature of maximum density for the most common models of water", Journal of Chemical Physics '''123''' 144504 (2005)] </ref>
| H<sub>2</sub>O || [[SPC]]  ||  228 || 1008 || Ref. 5
|-   
|-   
| H<sub>2</sub>O || [[SPC/E]]  || 241  || 1012 || <ref>[http://dx.doi.org/10.1080/0892702031000152172 Taras Bryk and A. D. J. Haymet "The Ice/Water Interface: Density-Temperature Phase Diagram for the SPC/E Model of Liquid Water", Molecular Simulation '''30''' pp. 131-135 (2004)]</ref>
| H<sub>2</sub>O || [[SPC/E]]  || 241  || 1012 || Ref. 6
|-   
|-   
| H<sub>2</sub>O || [[TIP3P]]  ||  182 || 1038 || <ref name="vegaAbascal"> </ref>
| H<sub>2</sub>O || [[TIP3P]]  ||  182 || 1038 || Ref. 5
|-   
|-   
| H<sub>2</sub>O || [[TIP4P]]  ||  253 || 1008 || <ref name="vegaAbascal"> </ref>
| H<sub>2</sub>O || [[TIP4P]]  ||  253 || 1008 || Ref. 5
|-   
|-   
| H<sub>2</sub>O || [[TIP4P/Ew]]  || 273  || 1000 || <ref>[http://dx.doi.org/10.1063/1.1683075    Hans W. Horn, William C. Swope,  Jed W. Pitera,      Jeffry D. Madura, Thomas J. Dick, Greg L. Hura and  Teresa Head-Gordon "Development of an improved four-site water model for biomolecular simulations: TIP4P-Ew", Journal of Chemical Physics '''120''' pp. 9665-9678 (2004)]</ref>
| H<sub>2</sub>O || [[TIP4P/Ew]]  || 273  || 1000 || Ref. 7
|-
|-
| H<sub>2</sub>O || [[TIP4P/Ice]]  ||  295 || 994  || <ref name="vegaAbascal"> </ref>
| H<sub>2</sub>O || [[TIP4P/Ice]]  ||  295 || 994  || Ref. 5
|-
|-
| H<sub>2</sub>O || [[TIP5P]]  ||  285 || 989 || <ref name="vegaAbascal"> </ref>
| H<sub>2</sub>O || [[TIP5P]]  ||  285 || 989 || Ref. 5
|-
|-
| H<sub>2</sub>O || [[TIP5P-E]]  ||  282 || 1004 || <ref>[http://dx.doi.org/10.1063/1.1652434 Steven W. Rick "A reoptimization of the five-site water potential (TIP5P) for use with Ewald sums", Journal of Chemical Physics '''120''' 6085 (2004)]</ref>
| H<sub>2</sub>O || [[TIP5P-E]]  ||  282 || 1004 || Ref. 8
|-
|-
| H<sub>2</sub>O || [[TIP4P/2005]]  ||  278 || 1000.5  || <ref>[http://dx.doi.org/10.1063/1.2121687    J. L. F. Abascal and C. Vega "A general purpose model for the condensed phases of water: TIP4P/2005", Journal of Chemical Physics, '''123''' 234505 (2005)]</ref>
| H<sub>2</sub>O || [[TIP4P/2005]]  ||  278 || 1000.5  || Ref. 9
|-
| H<sub>2</sub>O || [[TIP4PQ/2005]]  ||  280 ||  999.2  || <ref>[http://dx.doi.org/10.1063/1.3239471 E. G. Noya, C. Vega, L. M. Sesé, and R. Ramírez "Quantum effects on the maximum in density of water as described by the TIP4PQ/2005 model", Journal of Chemical Physics '''131''' 124518 (2009)]</ref>
|-
| H<sub>2</sub>O || [[TTM2.1-F model of water | TTM2.1-F]]  ||  273 ||  1038  || <ref>[http://dx.doi.org/10.1063/1.2759484  Francesco Paesani, Satoru Iuchi, and Gregory A. Voth "Quantum effects in liquid water from an ab initio-based polarizable force field", Journal of Chemical Physics '''127''' 074506 (2007)]</ref>
|-
| H<sub>2</sub>O || [[COS model of water |COS/B2]]  ||  170 ||  1076  || <ref name "KissBaranyai2012>[http://dx.doi.org/10.1063/1.4746419  Péter T. Kiss and András Baranyai "Density maximum and polarizable models of water", Journal of Chemical Physics '''137''' 084506 (2012)]</ref>
|-
| H<sub>2</sub>O || [[COS model of water |COS/G2]]  ||  255 ||  1013  || <ref name "KissBaranyai2012> </ref>
|-
| H<sub>2</sub>O || [[COS model of water |COS/G3]]  ||  195 ||  1042  || <ref name "KissBaranyai2012> </ref>
|-
| H<sub>2</sub>O || [[SWM4-DP model of water | SWM4-DP]]  ||  235 ||  1017  || <ref name "KissBaranyai2012> </ref>
|-
| H<sub>2</sub>O || [[SWM4-DP model of water | SWM4-NDP]]  ||  152 ||  1048  || <ref name "KissBaranyai2012> </ref>
|-
| H<sub>2</sub>O || [[BK water models | BKd1]]  ||  251 ||  1013  || <ref name "KissBaranyai2012> </ref>
|-
| H<sub>2</sub>O || [[BK water models | BKd2]]  ||  237 ||  1018  || <ref name "KissBaranyai2012> </ref>
|-
| H<sub>2</sub>O || [[BK water models | BKd3]]  ||  278 ||  999  || <ref name "KissBaranyai2012> </ref>
|-
|-
|}
|}
===References===
===References for water===
<references/>
#Felix Franks "Water A matrix of life", Royal Society of Chemistry 2nd Edition (2000) ISBN 978-0-85404-583-9  Table 3.5
;Related reading
#[http://dx.doi.org/10.1063/1.1681229  Frank H. Stillinger and Aneesur Rahman "Improved simulation of liquid water by molecular dynamics", Journal of Chemical Physics '''60''' pp. 1545-1557 (1974)]
*[http://dx.doi.org/10.1063/1.467029 S. R. Billeter, P. M. King, and W. F. van Gunsteren "Can the density maximum of water be found by computer simulation?", Journal of Chemical Physics '''100''' pp. 6692 (1994)]
#[http://dx.doi.org/10.1063/1.444325 William L. Jorgensen "Revised TIPS for simulations of liquid water and aqueous solutions", Journal of Chemical Physics '''77''' pp. 4156- (1982)]
#[http://dx.doi.org/10.1063/1.467029 S. R. Billeter, P. M. King, and W. F. van Gunsteren "Can the density maximum of water be found by computer simulation?", Journal of Chemical Physics '''100''' pp. 6692 (1994)]
#[http://dx.doi.org/10.1063/1.2056539 C. Vega and J. L. F. Abascal "Relation between the melting temperature and the temperature of maximum density for the most common models of water", Journal of Chemical Physics '''123''' 144504 (2005)]
#[http://dx.doi.org/10.1080/0892702031000152172 Taras Bryk and A. D. J. Haymet "The Ice/Water Interface: Density-Temperature Phase Diagram for the SPC/E Model of Liquid Water", Molecular Simulation '''30''' pp. 131-135 (2004)]
#[http://dx.doi.org/10.1063/1.1683075    Hans W. Horn, William C. Swope,  Jed W. Pitera,      Jeffry D. Madura, Thomas J. Dick, Greg L. Hura and  Teresa Head-Gordon "Development of an improved four-site water model for biomolecular simulations: TIP4P-Ew", Journal of Chemical Physics '''120''' pp. 9665-9678 (2004)]
#[http://dx.doi.org/10.1063/1.1652434 Steven W. Rick "A reoptimization of the five-site water potential (TIP5P) for use with Ewald sums", Journal of Chemical Physics '''120''' 6085 (2004)]
#[http://dx.doi.org/10.1063/1.2121687    J. L. F. Abascal and C. Vega "A general purpose model for the condensed phases of water: TIP4P/2005", Journal of Chemical Physics, '''123''' 234505 (2005)]
{{numeric}}
{{numeric}}
[[category: water]]
[[category: water]]
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