liquid–liquid critical point

A liquid–liquid critical point (or LLCP) is the endpoint of a liquid–liquid phase transition line (LLPT); it is a critical point where two types of local structures coexist at the exact ratio of unity. This hypothesis was first developed by Peter Poole, Francesco Sciortino, Uli Essmann and H. Eugene Stanley in Boston{{cite journal |author1=Poole, P. H. |author2=Sciortino, F. |author3=Essmann, U. |author4=Stanley, H. E. |year=1992 |title=Phase Behavior of Metastable Water |journal=Nature |volume=360 |issue=6402 |pages=324–328 |bibcode=1992Natur.360..324P |doi=10.1038/360324a0|s2cid=4302774 }} to obtain a quantitative understanding of the huge number of anomalies present in water.{{cite web |url=http://www1.lsbu.ac.uk/water/water_anomalies.html |accessdate = 30 August 2015 |title=Anomalous properties of water}}

Near a liquid–liquid critical point, there is always a competition between two alternative local structures. For instance, in supercooled water, two types of local structures have been predicted: a low-density local configuration (LD) and a high-density local configuration (HD), so above the critical pressure, the liquid is composed by a majority of HD local structure, while below the critical pressure a higher fraction of LD local configurations is present. The ratio between HD and LD configurations is determined according to the thermodynamic equilibrium of the system, which is often governed by external variables such as pressure and temperature.{{cite journal |author1=Holten, V. |author2=Palmer, J. C. |author3=Poole, P. H. |author4=Debenedetti, P. G. |author5=Anisimov, M. A. |year=2014 |title=Two-state thermodynamics of the ST2 model for supercooled water |journal=J. Chem. Phys. |volume= 140 |issue=10 |pages=104502 |doi=10.1063/1.4867287 |pmid=24628177 |bibcode=2014JChPh.140b4502M |arxiv=1312.4871|s2cid=18158514 }}

The liquid–liquid critical point theory can be applied to several liquids that possess the tetrahedral symmetry. The study of liquid–liquid critical points is an active research area with hundreds of articles having been published, though only a few of these investigations have been experimental{{cite journal |author1=Mishima, O. |author2=Stanley, H. E. |year=1998 |title=Decompression-Induced Melting of Ice IV and the Liquid–Liquid Transition in Water |journal=Nature |volume=392 |issue=6672 |pages=164–168 |bibcode=1998Natur.392..164M |doi=10.1038/32386|s2cid=4388755 }}{{cite journal |author1=Vasisht, V. V. |author2=Saw, S. |author3=Sastry, S. |year=2011 |title=Liquid–Liquid Critical Point in Supercooled Silicon |journal=Nat. Phys. |volume= 7 |issue=7 |pages=549–555 |doi=10.1038/nphys1993 |arxiv=1103.3473 |bibcode=2011NatPh...7..549V|s2cid=118861818 }}{{cite journal |author1=Katayama, Y. |author2=Mizutani, T. |author3=Utsumi, W. |author4=Shimomura, O. |author5=Yamakata, M. |author6=Funakoshi, K. |title=A First-Order Liquid–Liquid Phase Transition in Phosphorus |journal=Nature |year=2000 |volume=403 |issue=6766 |pages=170–173 |bibcode=2000Natur.403..170K |doi=10.1038/35003143 |pmid=10646596 |s2cid=4395377 }}{{cite journal |author1=Cadien, A. |author2=Hu, Q. Y. |author3=Meng, Y. |author4=Cheng, Y. Q. |author5=Chen, M. W. |author6=Shu, J. F. |author7=Mao, H. K. |author8=Sheng, H. W. |title=First-Order Liquid–Liquid Phase Transition in Cerium |journal=Phys. Rev. Lett. |year=2013 |volume=110 |issue=12 |pages=125503 |bibcode=2013PhRvL.110l5503C |pmid=25166820 |doi=10.1103/PhysRevLett.110.125503 |doi-access=free }}{{cite journal |author1=Yen, F. |author2=Chi, Z. H. |author3=Berlie, A. |author4=Liu, X. D. |author5=Goncharov, A. F. |title=Dielectric Anomalies in Crystalline Ice: Indirect Evidence of the Existence of a Liquid−Liquid Critical Point in H₂O |journal=J. Phys. Chem. C |year=2015 |volume=119 |issue=35 |pages=20618–20622 |doi=10.1021/acs.jpcc.5b07635 |arxiv=1501.02380|s2cid=102225912 }}{{Cite journal |last1=Gomes |first1=Gabriel O. |last2=Stanley |first2=H. Eugene |last3=Souza |first3=Mariano de |date=2019-08-19 |title=Enhanced Grüneisen Parameter in Supercooled Water |journal=Scientific Reports |language=en |volume=9 |issue=1 |page=12006 |doi=10.1038/s41598-019-48353-4 |pmid=31427698 |pmc=6700159 |arxiv=1808.00536 |bibcode=2019NatSR...912006O |issn=2045-2322 |doi-access=free}} since most modern probing techniques are not fast and/or sensitive enough to study them.