A closure for the two‐particle BGY equation is formulated by coupling the three‐particle distribution functions for the superposition approximation and the exact expression for rigid rods through a density and angle dependent quantity f( ρ,θ)=Ψ( ρ)χ(θ). Given the angle dependence, one can determine Ψ( ρ) by requiring that the virial theorem and the compressibility relation yield the same equation of state (pressure consistency). Fourth through tenth virial coefficients for rigid disks and spheres are calculated using this closure.
REFERENCES
1.
J. Yvon, Actualitiés Scientifiques et Industriel (Hermann, Paris, 1935), Vol. 203:
2.
See for example, T. Hill, Statistical Mechanics (McGraw‐Hill, New York, 1956);
J. E. Mayer, Handbuch derPhysik (Springer, Berlin, 1959), Vol. 12, p. 154.
3.
4.
English translation:
Sov. Phys.‐Dokl.
5
, 761
(1960–1961
).5.
Much of the literature regarding numerical investigations has been cited by C. A. Croxton, Liquid State Physics (Cambridge University, London, 1974);
A. Munster, Statistical Thermodynamics (Springer, Berlin, 1969, 1974) Vols. 1 and 2, respectively;
6.
7.
8.
9.
10.
Y.
Uehara
, Y.‐T.
Lee
, T.
Ree
, and F. H.
Ree
, J. Chem. Phys.
70
, 1884
(1979
).11.
12.
R. F.
Kayser
, H. J.
Raveché
, and W. W.
Wood
, J. Chem. Phys.
69
, 4617
(1978
).13.
14.
15.
16.
17.
18.
A. D. J.
Haymet
, S. A.
Rice
, and W. G.
Madden
, J. Chem. Phys.
74
, 3033
(1981
).19.
A. D. J.
Haymet
, S. A.
Rice
, and W. G.
Madden
, J. Chem. Phys.
75
, 4696
(1981
).20.
21.
J. M. J.
Van Leeuwen
, J.
Groeneveld
, and J.
De Boer
, Physica
25
, 792
(1959
);22.
K. A.
Green
, K. D.
Luks
, and J. J.
Kozak
, Phys. Rev. Lett.
42
, 985
(1979
);K. A.
Green
, K. D.
Luks
, and J. J.
Kozak
, Phys. Rev. A
21
, 356
(1980
).23.
24.
Z. W.
Salsburg
, R. W.
Zwanzig
, and J. G.
Kirkwood
, J. Chem. Phys.
21
, 1098
(1953
).25.
26.
T. Hill, Ref. 2, Chap. 6.
27.
F. H.
Ree
, R. N.
Keeler
, and S. L.
McCarthy
, J. Chem. Phys.
44
, 3407
(1966
).28.
29.
30.
31.
32.
33.
34.
35.
This content is only available via PDF.
© 1984 American Institute of Physics.
1984
American Institute of Physics
You do not currently have access to this content.
