Abstract
We consider the novel properties of the Stell–Hemmer core-softened potentials. First we explore how the theoretically predicted second critical point for these potentials is related to the occurrence of the experimentally observed solid–solid isostructural critical point. We then discuss how this class of potentials can generate anomalies analogous to those found experimentally in liquid water.
Similar content being viewed by others
REFERENCES
P. C. Hemmer and G. Stell, Phys. Rev. Lett. 24:1284 (1970).
J. Rowlinson and B. Widom, J. Chem. Phys. 52:1670 (1970).
M. Kac, G. E. Uhlenbeck, and P. C. Hemmer, J. Math. Phys. 4:216 (1963).
J. S. Høye and P. C. Hemmer, Phys. Norvegica 7:1 (1973).
A. Jayaramen, Phys. Rev. A 137:179 (1965).
Y. Yoshimura, Ber. Bunsenges. Phys. Chem. 95:135 (1991).
M. R. Sadr-Lahijany, A. Scala, S. V. Buldyrev, and H. E. Stanley, Phys. Rev. Lett. 81:4895 (1998); M. R. Sadr-Lahijany, A. Scala, S. V. Buldyrev, and H. E. Stanley, Phys. Rev. E 60:6714 (1999); A. Scala, M. R. Sadr-Lahijany, N. Giovambattista, S. V. Buldyrev, and H. E. Stanley, Waterlike anomalies for core-softened models of fluids: Two Dimensions, in preparation.
J. M. Kincaid, G. Stell, and C. K. Hall, J. Chem. Phys. 65:2161 (1976); J. M. Kincaid, G. Stell, and E. Goldmark, J. Chem. Phys. 65:2172 (1976); J. M. Kincaid and G. Stell, J. Chem. Phys. 67:420 (1977); C. K. Hall and G. Stell, Phys. Rev. A 7:1679 (1973).
R. I. Beecroft and C. A. Swenson, J. Phys. Chem. Sol. 15:234 (1960); B. L. Davis and L. H. Adams, J. Phys. Chem. Sol. 25:379 (1964); A. Jayaraman, Phys. Rev. Sec. A 137:179 (1965); J. M. Lawrence, M. C. Croft, and R. D. Parks, Phys. Rev. Lett. 35:289 (1975).
R. Sternheimer, Phys. Rev. 78:235 (1950); T. H. Hall, L. Merril, and J. D. Barnett, Science 146:1297 (1964); A. Jayaraman, Phys. Rev. 159:527 (1967); A. Jayaraman, Ann. Rev. Mat. Sci. 2:121 (1972); M. B. Maple and D. Wohlleben, AIP Conf. Proc. 18:447 (1974); P. W. Anderson and S. T. Chui, Phys. Rev. B 9:3229 (1975); A. Jayaraman, P. Dernier, and L. D. Longinotti, Phys. Rev. B 11:2783 (1975); A. W. Lawson and Ting-Yuan Tang, Phys. Rev. 76:301 (1949); A. F. Schuch and J. H. Sturdivant, J. Chem. Phys. 18:145 (1950); C. J. McHargue and H. Y. Yakel, Jr., Acta Metall. 8:637 (1960); M. Wilkinson, H. Child, C. McHargue, W. Koehler, and F. Wollan, Phys. Rev. 122:1409 (1961); R. Ramirez and L. M. Falivov, Phys. Rev. B 3:2425 (1975); L. F. Bates and M. M. Newmann, Proc. Phys. Soc. London 72:345 (1958).
K. K. Mon, N. W. Ashcroft, and G. V. Chester, Phys. Rev. B 19:5103 (1979).
I. Yokoyama and S. Ono, J. Phys. F: Met. Phys. 15:1215 (1985); K. Hoshino, C. H. Leung, I. L. McLaughlin, S. M. M. Rahman, and W. H. Young, J. Phys. F: Met. Phys. 17:787 (1987).
G. Stell and P. C. Hemmer, J. Chem. Phys. 56:4274 (1972).
P. G. Debenedetti, Metastable Liquids (Princeton University Press, Princeton, 1996); P. G. Debenedetti, V. S. Raghavan, and S. S. Borick, J. Phys. Chem. 95:4540 (1991); P. G. Debenedetti and M. C. Dantonio, AICHE J. 34:447 (1988).
H. Takahashi, Proc. Phys. Math. Soc. Jpn. 24:60 (1942); Mathematical Physics in One Dimension, E. H. Lieb and D. C. Mattis, eds. (Academic, New York, 1966), pp. 25-34.
T. Head-Gordon and F. H. Stillinger, J. Chem. Phys. 98:3313 (1993).
A. Ben-Naim, Statistical Thermodynamics for Chemists and Biochemists (Plenum Press, New York, 1992), pp. 233–238; C. H. Cho et al., Phys. Rev. Lett. 76:1651 (1996); M. Canpolat, F. W. Starr, A. Scala, M. R. Sadr-Lahijany, O. Mishima, S. Havlin, and H. E. Stanley, Chem. Phys. Lett. 294:9 (1998).
P. H. Poole, F. Sciortino, U. Essman, and H. E. Stanley, Nature 360:324 (1992); Phys. Rev. E 48:4605 (1993); the occurrence of a liquid_liquid critical point has indeed been observed for liquid phosphorus by Y. Katayama et al., Nature 403:170 (2000) and foot-note written by O. Mishima, Phys. Rev. Lett. 85:334 (2000).
D. A. Young and B. J. Alder, Phys. Rev. Lett. 38:1213 (1977); D. A. Young and B. J. Alder, J. Chem. Phys. 70:473 (1979).
E. A. Jagla, Phys. Rev. E 58:1478 (1998).
F. X. Prielmeier, E. W. Lang, R. J. Speedy, and H.-D. Lüdemann, Phys. Rev. Lett. 59:1128 (1987); Ber. Bunsenges. Phys. Chem. 92:1111 (1988); L. Haar, J. S. Gallagher, and G. S. Kell, NBS/NRC Steam Tables. Thermodynamic and Transport Properties and Computer Programs for Vapor and Liquid States of Water in SI Units (Hemisphere Publishing Co., Washington, D.C., 1984), pp. 271-276.
S. Sastry, P. Debenedetti, F. Sciortino, and H. E. Stanley, “Singularity-Free Interpretation of the Thermodynamics of Supercooled Water,” Phys. Rev. E 53:6144–6154 (1996).
A. Scala, F. W. Starr, E. La Nave, F. Sciortino, and H. E. Stanley, Configurational entropy and diffusivity of supercooled water, Nature 406:166 (2000); E. La Nave, A. Scala, F. W. Starr, F. Sciortino, and H. E. Stanley, Instantaneous normal mode analysis of supercooled water, Phys. Rev. Lett. 84:4605 (2000).
F. W. Starr, S. Harrington, F. Sciortino, and H. E. Stanley, Phys. Rev. Lett. 82:3629 (1999); F. W. Starr, F. Sciortino, and H. E. Stanley, Phys. Rev. E 60:6757 (1999).
F. H. Stillinger and D. K. Stillinger, Physica A 244:358 (1997); F. H. Stillinger and T. A. Weber, J. Chem. Phys. 68:3837 (1978); 74:4015 (1981).
G. Adam and J. H. Gibbs, J. Chem. Phys. 43:139 (1965).
O. Mishima and H. E. Stanley, Nature 396:329 (1998).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Scala, A., Sadr-Lahijany, M.R., Giovambattista, N. et al. Applications of the Stell–Hemmer Potential to Understanding Second Critical Points in Real Systems. Journal of Statistical Physics 100, 97–106 (2000). https://doi.org/10.1023/A:1018631426614
Issue Date:
DOI: https://doi.org/10.1023/A:1018631426614