×

Analytic equation of state for the exponential-six fluids based on the Ross variational perturbation theory. (English) Zbl 1029.82502

Summary: An analytic expression of radial distribution function of hard spheres is developed in terms of a polynomial expansion of nonlinear base functions and the Carnahan-Starling equation of state (EOS). The comparison with the Monte-Carlo data and the Percus-Yevick expression shows that the expression developed gives out better results. The expression is very simple that can make most perturbation theories become analytic ones, and a simple analytic EOS for the fluids with continuous exponential-six potential is established based on the Ross variational perturbation theory. The main thermodynamic quantities have been analytically derived, the resulting expressions are surprisingly simple, the variational procedure is greatly simplified and the calculations are absolutely convergent. The numerical results are compared with the Monte-Carlo data and the original non-analytic theory. It is shown that the precision of the analytic EOS is as good as the original non-analytic one.

MSC:

82B30 Statistical thermodynamics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Barker, J. A.; Henderson, D., J. Chem. Phys., 47, 4714 (1967)
[2] Weeks, J. D.; Chandler, D.; Andersen, H. C., J. Chem. Phys., 54, 5237 (1971)
[3] Ross, M., J. Chem. Phys., 71, 1567 (1979)
[4] Carnahan, N. F.; Starling, K. E., J. Chem. Phys., 51, 635 (1969)
[5] Wertheim, M. S., Phys. Rev. Lett., 10, 321 (1963)
[6] Thiele, E., J. Chem. Phys., 39, 474 (1963)
[7] Troop, G. J.; Bearman, R. J., J. Chem. Phys., 42, 2408 (1965)
[8] Anderson, H. C.; Chandler, D., J. Chem. Phys., 55, 1497 (1971)
[9] White, J. A., J. Chem. Phys., 113, 1580 (2000)
[10] Smith, W. R.; Henderson, D., Mol. Phys., 19, 411 (1970)
[11] Chang, J.; Sandler, S. I., Mol. Phys., 81, 735 (1994)
[12] Bravo Yuste, S.; Santos, A., Phys. Rev. A, 43, 5418 (1991)
[13] Bravo Yuste, S.; López de Haro, M.; Santos, A., Phys. Rev. E, 53, 4820 (1996)
[14] Tang, Y.; Lu, C.-Y., J. Chem. Phys., 100, 6665 (1994)
[15] Largo, J.; Solana, J. R., Fluid Phase Equil., 167, 21 (2000)
[16] Largo, J.; Solana, J. R., Int. J. Thermophys., 21, 899 (2000)
[17] Ross, M.; Ree, F. H.; Young, D. A., J. Chem. Phys., 79, 487 (1983)
[18] Holmcs, N. C.; Ross, M.; Ncllis, W. L., Phys. Rev. B, 52, 15835 (1995)
[19] Tang, Y., J. Chem. Phys., 116, 6694 (2002)
[20] Tang, Y.; Lu, B. C.-Y., J. Chem. Phys., 100, 6665 (1994)
[21] Tang, Y.; Wang, Z.; Lu, B. C.-Y., Mol. Phys., 99, 65 (2001)
[22] Kolafa, J., quoted by T. Boublik, Mol. Phys., 59, 371 (1986)
[23] Mulero, A.; Galán, C.; Cuadros, F., J. Chem. Phys., 111, 4186 (1999)
[24] Ree, F. H., J. Chem. Phys., 64, 4601 (1976)
[25] Barker, J. A.; Henderson, D., Mol. Phys., 21, 187 (1971)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.