Density fluctuations and the structure of a nonuniform hard sphere fluid

Physical Review Letters

Volumn 86, Issue 3, 2001, Pages 440-443

  Katsov, Kirill ^a   Weeks, John D ^a,b  

^a UNIVERSITY OF MARYLAND   (United States)

^b University of Maryland   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; CORRELATION METHODS; DENSITY OF LIQUIDS; HYDROPHOBICITY; INTEGRAL EQUATIONS; LIQUIDS; PHASE INTERFACES; SPHERES; STRUCTURE (COMPOSITION); THERMODYNAMICS; VAPORS;

HYDROSTATIC APPROXIMATION; HYDROSTATIC DENSITY; MODIFIED CHEMICAL POTENTIAL; NONUNIFORM HARD SPHERE FLUID; PERCUS-YEVICK EQUATION;

FLUIDS;

EID: 0035121025     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.86.440     Document Type: Article

References (21)

1. See, e.g., J. S. Rowlinson and B. Widom, Molecular Theory of Capillarity (Oxford Press, Oxford, 1989).
2. See, e.g., J. P. Hansen and I. R. McDonald. Theory of Simple Liquids (Academic Press, London, 1986).
3. J. K. Percus, Phys. Rev. Lett. 8, 462 (1962).
4. J. D. Weeks, R. L. B. Selinger, and J. Q. Broughton, Phys. Rev. Lett. 75, 2694 (1995).
5. J. D. Weeks, K. Vollmayr, and K. Katsov, Physica (Amsterdam) 244A, 461 (1997).
6. J. D. Weeks, K. Katsov, and K. Vollmayr, Phys. Rev. Lett. 81, 4400 (1998).
7. J. K. Percus, in The Equilibrium Theory of Classical Fluids, edited by H. L. Frisch and J. L. Lebowitz (W.A. Benjamin, Inc., New York, 1964), p. II-33.
8. E. Waisman, Mol. Phys. 25, 45 (1973).
9. D. Chandler, Phys. Rev. E 48, 2898 (1993).
10. G. E. Crooks and D. Chandler, Phys. Rev. E 56, 4217 (1997).
11. K. Vollmayr-Lee, K. Katsov, and J. D. Weeks, J. Chem. Phys. (to be published).
12. K. Katsov and J. D. Weeks (to be published); K. Katsov, K. Vollmayr-Lee, and J. D. Weeks (to be published).
13. K. Katsov and J. D. Weeks (to be published); K. Katsov, K. Vollmayr-Lee, and J. D. Weeks (to be published).
14. For a general potential, Eq. (6) does not reduce to the usual HNC closure, nor does Eq. (5) reduce to the usual PY closure.
15. We performed standard canonical (NVT) ensemble Monte Carlo simulations for a hard sphere fluid subject to the various external fields with N ranging from 500 to 2500 particles.
16. D. M. Huang and D. Chandler, Phys. Rev. E 61, 1501 (2000).
17. Since we can determine the density response to a general external field, it is straightforward to calculate the free energy of a nonuniform hard sphere system by numerical integration using a coupling parameter method. Further discussion of this point and of the relation to density functional theory (DFT) will be given in future work. Here we mention only that in DFT the nonuniform density ρ(r) is usually related to that of a uniform fluid at some much smoother weighted or coarse-grained density ρ̄(r). This coarse graining builds in nonlocal effects associated with excluded volume correlations and is required since the local value of the full density ρ(r) can quite easily exceed the close packed density tor the uniform system. In practice many different and often quite complicated weighting schemes have been proposed. In contrast our approach using Eq. (5) starts from properties of the uniform fluid at the local hydrostatic density of Eq. (1), very simply determined from the local value of the external field φ(r), and builds in nonlocal effects systematically from a self-consistent application of linear response theory at every point r.
18. L. R. Pratt and D. Chandler, J. Chem. Phys. 67, 3683 (1977).
19. G. Hummer et al., Proc. Natl. Acad. Sci. U.S.A. 93, 8951 (1996).
20. K. Lum, D. Chandler, and J. D. Weeks, J. Phys. Chem. B 103, 4570 (1999).
21. One can also derive Eq. (5) from this perspective, generalizing Ref. [9]. See K. Katsov, Ph.D. thesis, University of Maryland, 2000 and Ref. [12].