Abstract
The pressure versus temperature phase diagram of a system of particles interacting through a multiscale shoulder-like potential is exactly computed in one dimension. The N-shoulder potential exhibits N density anomaly regions in the phase diagram if the length scales can be connected by a convex curve. The result is analyzed in terms of the convexity of the Gibbs free energy.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
P. C. Hemmer and G. Stell, Fluids with Several Phase Transitions, Phys. Rev. Lett., 24(23), 1284 (1970)
P. G. Debenedetti, V. S. Raghavan, and S. S. Borick, Spinodal curve of some supercooled liquids, J. Chem. Phys., 95(11), 4540 (1991)
S. Sastry, P. G. Debenedetti, F. Sciortino, and H. E. Stanley, Singularity-free interpretation of the thermodynamics of supercooled water, Phys. Rev. E, 53(6), 6144 (1996)
C. J. Roberts and P. G. Debenedetti, Polyamorphism and density anomalies in network-forming fluids: Zeroth-and first-order approximations, J. Chem. Phys., 105(2), 658 (1996)
E. A. Jagla, Phase behavior of a system of particles with core collapse, Phys. Rev. E, 58(2), 1478 (1998)
G. Franzese, G. Malescio, A. Skibinsky, S. V. Buldyrev, and H. E. Stanley, Generic mechanism for generating a liquid–liquid phase transition, Nature, 409(6821), 692 (2001)
N. B. Wilding and J. E. Magee, Phase behavior and thermodynamic anomalies of core-softened fluids, Phys. Rev. E, 66(3), 031509 (2002)
P. Camp, Structure and phase behavior of a twodimensional system with core-softened and long-range repulsive interactions, Phys. Rev. E, 68(6), 061506 (2003)
M. Pretti and C. Buzano, Thermodynamic anomalies in a lattice model of water, J. Chem. Phys., 121(23), 11856 (2004)
A. Balladares and M. C. Barbosa, Density anomaly in core-softened lattice gas, J. Phys.: Condens. Matter, 16(49), 8811 (2004)
A. B. Oliveira and M. C. Barbosa, Density anomaly in a competing interactions lattice gas model, J. Phys.: Condens. Matter, 17(3), 399 (2005)
Yu. D. Fomin, E. N. Tsiok, and V. N. Ryzhov, Complex phase behavior of the system of particles with smooth potential with repulsive shoulder and attractive well, J. Chem. Phys., 134(4), 044523 (2011)
G. S. Kell, Precise representation of volume properties of water at one atmosphere, J. Chem. Eng. Data, 12(1), 66 (1967)
P. H. Poole, F. Sciortino, U. Essmann, and H. E. Stanley, Phase behaviour of metastable water, Nature, 360(6402), 324 (1992)
J. C. Palmer, F. Martelli, Y. Liu, R. Car, A. Z. Panagiotopoulos, and P. G. Debenedetti, Metastable liquid–liquid transition in a molecular model of water, Nature, 510(7505), 385 (2014)
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)
J. A. Sellberg, C. Huang, T. A. McQueen, N. D. Loh, H. Laksmono, et al., Ultrafast X-ray probing of water structure below the homogeneous ice nucleation temperature, Nature, 510, 381 (2014)
H. Takahashi, Mathematical Physics in One Dimension, Academic Press, 1966, pp 25–34
G. Gallavotti, Statistical Mechanics: A Short Treatise, Berlin: Springer, 1999, pp 162–164
A. Barros de Oliveira, P. A. Netz, T. Colla, and M. C. Barbosa, Thermodynamic and dynamic anomalies for a three-dimensional isotropic core-softened potential, J. Chem. Phys., 124(8), 084505 (2006)
A. Barros de Oliveira, P. A. Netz, T. Colla, and M. C. Barbosa, Thermodynamic and dynamic anomalies for a three-dimensional isotropic core-softened potential, J. Chem. Phys., 124(8), 084505 (2006)
E. Barraz Salcedo, and M. C. Barbosa, Thermodynamic, dynamic, and structural anomalies for shoulderlike potentials, J. Chem. Phys., 131(9), 094504 (2009)
M. A. A. Barbosa, E. Salcedo, and M. C. Barbosa, Multiple liquid-liquid critical points and density anomaly in core-softened potentials, Phys. Rev. E, 87(3), 032303 (2013)
M. A. A. Barbosa, F. V. Barbosa, and F. A. Oliveira, Thermodynamic and dynamic anomalies in a onedimensional lattice model of liquid water, J. Chem. Phys., 134(2), 024511 (2011)
F. B. V. da Silva, F. A. Oliveira, and M. A. A. Barbosa, Residual entropy and waterlike anomalies in the repulsive one dimensional lattice gas, J. Chem. Phys., 142(14), 144506 (2015)
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Rizzatti, E.O., Barbosa, M.A.A. & Barbosa, M.C. Core-softened potentials, multiple liquid–liquid critical points, and density anomaly regions: An exact solution. Front. Phys. 13, 136102 (2018). https://doi.org/10.1007/s11467-017-0725-3
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11467-017-0725-3