Fundamental-measure free-energy density functional for hard spheres: Dimensional crossover and freezing

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 55, Issue 4, 1997, Pages 4245-4263

  Rosenfeld, Y ^a   Schmidt, M ^b   Lowen H ^b   Tarazona, P ^c  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

^b HEINRICH HEINE UNIVERSITY   (Germany)

^c UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4043107549     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.55.4245     Document Type: Article

References (74)

1. For a recent review, see Density Functional Theory, Vol. 337 of NATO Advanced Study Institute, Series B: Physics, edited by E.K.U. Gross and R.M. Drexler (Plenum Press, New York, 1995).
2. H. Löwen, Phys. Rep. 237, 249 (1994).
3. See the recent collection of reviews, Fundamentals of Inhomogeneous Fluids, edited by D. Henderson (Dekker, New York, 1992), and in particular the review by R. Evans.
4. J.P. Hansen and I.R. McDonald, Theory of Simple Liquids, 2nd ed. (Academic Press, London, 1986).
5. B.K. Peterson, K. Gubbins, G.S. Heffelfinger, U. Marini Bettolo Marconi and F. van Swol, J. Chem. Phys. 88, 6487 (1988).
6. Molecular Dynamics in Restricted Geometries, edited by J. Klafter and J.M. Drake (John Wiley, New York, 1989).
7. H.K. Christenson, Phys. Rev. Lett. 74, 4675 (1995).
8. M. Schmidt and H. Löwen, Phys. Rev. Lett. 76, 4522 (1996);
9. Martin Schoen, J. Chem. Phys. 101, 6865 (1994).
10. See, for example, T. Fehr and H. Löwen, Phys. Rev. E 52, 4016 (1995).
11. M. Krech, The Casimir Effect in Critical Systems (World Scientific, Singapore, 1995).
12. J.A. Duffy, N.J. Wilkinson, H.M. Fretwell, M.A. Alam and R. Evans, J. Phys. Condens. Matter 7, L713 (1995).
13. P. Pieranski, L. Strzelcki and B. Pansu, Phys. Rev. Lett. 50, 900 (1983).
14. D.H. van Winkle and C.A. Murray, Phys. Rev. A 34, 562 (1986);
15. C.A. Murray, W.O. Sprenger and R.A. Wenk, Phys. Rev. B 42, 688 (1990);
16. C.A. Murray, in Bond-Orientational Order in Condensed Matter Systems, edited by K.J. Strandburg (Springer, New York, 1992).
17. G. Martinelli Kepler and S. Fraden, Langmuir 10, 2501 (1994).
18. J. Weis, D.W. Oxtoby, D.G. Grier and C.A. Murray, J. Chem. Phys. 103, 1180 (1995).
19. J.C. Crocker and D.G. Grier, Phys. Rev. Lett. 73, 352 (1994).
20. G. Martinelli Kepler and S. Fraden, Phys. Rev. Lett. 73, 356 (1994).
21. D.G. Grier and C.A. Murray, J. Chem. Phys. 100, 9088 (1994).
22. G. Rodriguez and L. Vicente, Mol. Phys. 87, 213 (1996).
23. C.N. Patra and S.K. Ghosh, Phys. Rev. 50, 5123 (1994).
24. J.E. Hug, F. van Swol and C.F. Zukowski, Langmuir 11, 111 (1995).
25. J.K. Percus, J. Stat. Phys. 23, 657 (1980).
26. M.S. Wertheim, L. Blum, and D. Bratko, in Micellar Solutions and Microemulsions: Structure, Dynamics, and Statistical Thermodynamics, edited by S.-H. Chen and R. Rajagopalan (Springer, New York, 1990).
27. T. Biben, R. Ohnesorge and H. Löwen, Europhys. Lett. 28, 665 (1994).
28. J.K. Percus, J. Stat. Phys. 15, 505 (1976).
29. J.K. Percus, J. Stat. Phys. 52, 1157 (1988).
30. P. Tarazona, Mol. Phys. 52, 81 (1984);
31. P. Tarazona, Phys. Rev. A 31, 2672 (1985).
32. See, e.g., the review by M. Baus, J. Phys. Condens. Matter 2, 2241 (1990).
33. R. Ohnesorge, H. Löwen and H. Wagner, Europhys. Lett. 22, 245 (1993);
34. R. Ohnesorge, H. Löwen and H. Wagner, Phys. Rev. E 50, 4801 (1994).
35. Y. Rosenfeld, in Chemical Applications of Density-Functional Theory, edited by B. Laird, R. Ross, and T. Ziegler, ACS Symposium Series Vol. 629 (American Chemical Society, Washington, DC, 1996), pp. 198–211; in Strongly Coupled Plasma Physics, edited by W. Kraeft and M. Schlanges (World Scientific, Singapore, 1996), pp. 27–36;
36. J. Phys. Condens. Matter 8, 9289 (1996).
37. Y. Rosenfeld, Phys. Rev. Lett. 63, 980 (1989);
38. Y. Rosenfeld, J. Chem. Phys. 93, 4305 (1990);
39. Y. Rosenfeld, D. Levesque and J.J. Weis, J. Chem. Phys.ibid. 92, 6818 (1990).
40. Y. Rosenfeld, Phys. Rev. E 50, R3318 (1994);
41. Y. Rosenfeld, Mol. Phys. 86, 637 (1995).
42. Y. Rosenfeld, Phys. Rev. A 42, 5978 (1990).
43. Y. Rosenfeld, J. Chem. Phys. 98, 8126 (1993);
44. Y. Rosenfeld, Phys. Rev. E 54, 2827 (1996).
45. Y. Rosenfeld, Phys. Rev. Lett. 72, 3831 (1994);
46. J. Phys. Chem. 99, 2857 (1995).
47. Y. Rosenfeld, M. Schmidt, H. Löwen and P. Tarazona, J. Phys. Condens. Matter 8, L577 (1996).
48. Y. Rosenfeld, Phys. Rev. A 32, 1834 (1985);
49. Y. Rosenfeld, Phys. Rev. A 33, 2025 (1986);
50. Y. Rosenfeld, Phys. Rev. E 47, 2676 (1993), and references therein.
51. Y. Rosenfeld and N.W. Ashcroft, Phys. Rev. A 20, 1208 (1979).
52. Y. Rosenfeld, J. Chem. Phys. 89, 4272 (1988).
53. J.K. Percus and G.J. Yevick, Phys. Rev. 110, 1 (1958);
54. J.L. Lebowitz, Phys. Rev. A 133, 895 (1964).
55. H. Reiss, H. Frisch and J.L. Lebowitz, J. Chem. Phys. 31, 369 (1959);
56. H. Reiss, J. Phys. Chem. 96, 4736 (1992).
57. E. Kierlik and M.L. Rosinberg, Phys. Rev. A 42, 3382 (1990).
58. E. Kierlik and M.L. Rosinberg, Phys. Rev. A 44, 5025 (1991); and private communication.
59. S. Phan, E. Kierlik, M.L. Rosinberg, B. Bildstein and G. Kahl, Phys. Rev. E 48, 618 (1993).
60. J. Jung, M.S. Jhon and F. Ree, J. Chem. Phys. 100, 528 (1994);
61. J. Jung, M.S. Jhon and F. Ree, J. Chem. Phys. 100, 9064 (1994).
62. K. Swamy independently confirmed the 1/r singularity.
63. F. Lado, J. Chem. Phys. 49, 3092 (1968).
64. Gaussians can be considered numerically as strictly confined only for relatively large values of α, but certainly for values which are relevant for describing the solid.
65. P. Tarazona (unpublished).
66. Y. Rosenfeld, J. Phys. Condens. Matter 8, L795 (1996).
67. For example, for classical plasmas of point charges in a uniform background pair correlation functions were obtained with (Formula presented) which are almost indistiguishable from the simulation results, and the energies agree to better than 0.1% (see Ref. 34 above). Yet the inverse compressibility, as obtained from integrating the direct correlation functions, deviates from that obtained from differentiating the energy equation of state by as much as 30% near freezing densities. With the new (Formula presented) similarly accurate results for the pair correlations are obtained, but this deviation is now reduced to only about 10% [Y. Rosenfeld (unpublished)]. In the case of the Lennard-Jones system both (Formula presented) and (Formula presented) yield pressures, energies, and inverse compressibilities all in about 1% agreement with the simulation data, yet the results using (Formula presented) are slightly better [Y. Rosenfeld (unpublished)]. It was found [Y. Rosenfeld and G. Kahl, J. Phys. Condens. Matter 9, L89 (1997)] that using (Formula presented) instead of (Formula presented) hardly affects the properties of the functional in applications to the inverse scattering problem as discussed in Ref. 56.
68. M. Schmidt and H. Löwen (unpublished).
69. J.A. Cuesta, Phys. Rev. Lett. 76, 3742 (1996).
70. A. Santos, M. Lopez de Haro and S. Bravo Yuste, J. Chem. Phys. 103, 4622 (1995).
71. W.G. Hoover and F.H. Ree, J. Chem. Phys. 49, 3609 (1968);
72. B.J. Alder, W.G. Hoover and D.A.Young, J. Chem. Phys.ibid. 49, 3688 (1968);
73. D.A. Young and B.J. Alder, J. Chem. Phys.ibid. 60, 1254 (1974).
74. G. Kahl, B. Bildstein, and Y. Rosenfeld, Phys. Rev. E 54, 5391 1996).