DOI: 10.1073/pnas.0507870102. Relation between the Widom line and the dynamic crossover in systems with a liquid

Relation between the Widom line and the dynamic crossover in systems with a liquid–liquid phase transition

10.1073/pnas.0507870102

Crossref journal-article

Proceedings of the National Academy of Sciences

Proceedings of the National Academy of Sciences (341)

Abstract

We investigate, for two water models displaying a liquid–liquid critical point, the relation between changes in dynamic and thermodynamic anomalies arising from the presence of the liquid–liquid critical point. We find a correlation between the dynamic crossover and the locus of specific heat maxima \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}C_{P}^{{\mathrm{max}}}\end{equation*}\end{document} (“Widom line”) emanating from the critical point. Our findings are consistent with a possible relation between the previously hypothesized liquid–liquid phase transition and the transition in the dynamics recently observed in neutron scattering experiments on confined water. More generally, we argue that this connection between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}C_{P}^{{\mathrm{max}}}\end{equation*}\end{document} and dynamic crossover is not limited to the case of water, a hydrogen bond network-forming liquid, but is a more general feature of crossing the Widom line. Specifically, we also study the Jagla potential, a spherically symmetric two-scale potential known to possess a liquid–liquid critical point, in which the competition between two liquid structures is generated by repulsive and attractive ramp interactions.

Bibliography

Xu, L., Kumar, P., Buldyrev, S. V., Chen, S.-H., Poole, P. H., Sciortino, F., & Stanley, H. E. (2005). Relation between the Widom line and the dynamic crossover in systems with a liquidâliquid phase transition. Proceedings of the National Academy of Sciences, 102(46), 16558â16562.

Authors 7

Limei Xu (first)
Pradeep Kumar (additional)
S. V. Buldyrev (additional)
S.-H. Chen (additional)
P. H. Poole (additional)
F. Sciortino (additional)
H. E. Stanley (additional)

References 41 Referenced 718

Debenedetti P. G. (1996) Metastable Liquids: Concepts and Principles (Princeton Univ. Press Princeton). (10.1515/9780691213941)
Levelt J. M. H. (1958) Ph.D. Thesis (Univ. of Amsterdam Van Gorkum & Co. Assen The Netherlands).
10.1016/S0031-8914(58)80093-2
10.1016/S0031-8914(58)80080-4
Anisimov M. A. Sengers J. V. & Levelt Sengers J. M. H. (2004) in Aqueous System at Elevated Temperatures and Pressures: Physical Chemistry in Water Stream and Hydrothermal Solutions eds. Palmer D. A. Fernandez-Prini R. & Harvey A. H. (Elsevier Amsterdam) pp. 29–71. (10.1016/B978-012544461-3/50003-X)
Robinson G. W. Zhu S.-B. Singh S. & Evans M. W. (1996) Water in Biology Chemistry and Physics: Experimental Overviews and Computational Methodologies (World Scientific Singapore). (10.1142/2923)
Bellissent-Funel M.-C. ed. (1999) Hydration Processes in Biology: Theoretical and Experimental Approaches (IOS Press Amsterdam).
10.1021/j100126a005
10.1088/0953-8984/15/45/R01
10.1016/S0378-4371(03)00012-8
10.1146/annurev.physchem.55.091602.094156
10.1103/PhysRevB.60.3169
10.1103/PhysRevLett.59.1128
Lang, E. W. & Lüdemann, H. D. (2004) Angew Chem. Intl. Ed. Engl. 21, 315–329. / Angew Chem. Intl. Ed. Engl. (2004)
10.1038/19042
10.1063/1.480241
10.1088/0953-8984/11/50/317
10.1103/PhysRevE.63.061509
10.1088/0953-8984/15/45/L03
10.1038/360324a0
10.1038/24540
10.1038/35055514
10.1103/PhysRevLett.91.155701
10.1038/35002027
10.1063/1.1832595
10.1103/PhysRevLett.95.117802
10.1038/35087524
10.1038/nmat994
10.1073/pnas.1233719100
10.1063/1.444325
10.1063/1.1678388
10.1103/PhysRevE.72.021501
10.1103/PhysRevLett.88.195701
10.1016/j.physa.2003.08.003
10.1103/PhysRevLett.94.217802
Götze W. (1991) in Liquids Freezing and Glass Transition eds. Hansen J. P. Levesque D. & Zinn-Justin J. (North–Holland Amsterdam) pp. 287–503.
10.1088/0953-8984/17/43/L01
10.1063/1.1696442
10.1063/1.433518
10.1038/35018034
Maruyama, S., Wakabayashi, K. & Oguni, M. (2004) Am. Inst. Phys. Conf. Proc. 708, 675–676. / Am. Inst. Phys. Conf. Proc. (2004)

Dates

Type	When
Created	19 years, 9 months ago (Nov. 2, 2005, 8:25 p.m.)
Deposited	3 years, 4 months ago (April 12, 2022, 2:08 p.m.)
Indexed	2 weeks, 1 day ago (Aug. 6, 2025, 8:01 a.m.)
Issued	19 years, 9 months ago (Nov. 2, 2005)
Published	19 years, 9 months ago (Nov. 2, 2005)
Published Online	19 years, 9 months ago (Nov. 2, 2005)
Published Print	19 years, 9 months ago (Nov. 15, 2005)

Funders 0

None

BibTeX

@article{Xu_2005, title={Relation between the Widom line and the dynamic crossover in systems with a liquid–liquid phase transition}, volume={102}, ISSN={1091-6490}, url={http://dx.doi.org/10.1073/pnas.0507870102}, DOI={10.1073/pnas.0507870102}, number={46}, journal={Proceedings of the National Academy of Sciences}, publisher={Proceedings of the National Academy of Sciences}, author={Xu, Limei and Kumar, Pradeep and Buldyrev, S. V. and Chen, S.-H. and Poole, P. H. and Sciortino, F. and Stanley, H. E.}, year={2005}, month=nov, pages={16558–16562} }

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