On the relation between the compressibility and the static structure factor of a fluid with a state-dependent pair-potential

Journal of Chemical Physics

Volumn 118, Issue 2, 2003, Pages 892-896

  Tejero, C F ^a   Baus, M ^b  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

COMPRESSIBILITY OF LIQUIDS; COMPUTER SIMULATION; FOURIER TRANSFORMS; FREE ENERGY; HAMILTONIANS; KINETIC ENERGY; NUMERICAL ANALYSIS; POTENTIAL ENERGY; STRUCTURE (COMPOSITION); THERMODYNAMIC PROPERTIES;

INFINITE WAVELENGTH LIMIT; STATE DEPENDENT PAIR POTENTIAL; STATIC STRUCTURE FACTOR;

FLUIDS;

EID: 0037425681     PISSN: 00219606     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1526837     Document Type: Article

References (14)

1. C. N. Likos, Phys. Rep. 348, 267 (2001), and references therein.
2. A. König and N. W. Ashcroft, Phys. Rev. E 63, 041203 (2001).
3. Note that when the densities of the different constituents can be varied independently, the density dependence of the effective potential can be transformed away by working in the semi-grand ensemble as illustrated in, e.g., M. Dijkstra, R. van Roij and R. Evans, Phys. Rev. E 59, 5744 (1999).
4. A. A. Louis, J. Phys.: Condens. Matter 14, 9187 (2002).
5. R. Evans, Adv. Phys. 28, 143 (1979).
6. J. P. Hansen and I. R. McDonald, Theory of Simple Liquids, 2nd ed. (Academic, London, 1986).
7. D. A. McQuarrie, Statistical Mechanics (Harper & Row, New York, 1976).
8. Of course, in many cases this condition of thermodynamic consistency has already been verified numerically.
9. Approximate integral equation theories for complex fluids should be generalized in the same way and then be closed with the generalized Ornstein-Zernike equation (29).
10. The crucial point her is again provided by Eq. (36). If Eq. (36) was evaluated with c(r;ρ";[V(ρ")]), the compressibility equation (Eq. (20)) would hold but the theory would not be thermodynamically consistent [i.e., Eq. (15) would not hold]. Our treatment favors thus the latter property over the former one. That a problem should arise with Eq. (20) can also be inferred from the standard textbook derivation (cf. Ref. 6) of the compressibility equation since the latter is based on derivatives with respect to the fugacity which now also operate on the effective potential.
11. N. G. Almarza, E. Lomba, G. Ruiz, and C. F. Tejero, Phys. Rev. Lett. 86, 2038 (2001).
12. C. F. Tejero and M. Baus, Phys. Rev. E 57, 4821 (1998).
13. M. Dijkstra and R. van Roij, J. Phys.: Condens. Matter 10, 1219 (1998).
14. After this paper was sumitted we did learn about related work [F. Stillinger, H. Sakai, and S. Torquato, J. Chem. Phys. 117, 288 (2002)] where similar conclusions were reached.