The evolution of multicomponent systems at high pressures Part III. Effects of particle shape upon the Alder–Wainwright transition

Abstract

The thermodynamic stability of pure, aspherical hard-body fluids has been examined throughout the range of pressure 1–100000 atm, and over a range of temperature extending from 10 to 10000 K, using the equation of state developed from scaled particle theory (SPT) by Boublík for convex, aspherical, hard-body systems (T. Boublík, J. Chem. Phys., 1975, 63, 4084). The scaled particle theory description of the spherical hard-body system is an exact solution in statistical mechanics, as is also its extension to aspherical hard bodies. Therefore, the Boublík solutions share the absolute property of scaled particle theory. Accordingly, the constraints of the third law of thermodynamics have been applied to this analysis of the thermodynamic stability of aspherical hard-body fluids. Aspherical hard-body fluids are shown to undergo the Alder–Wainwright transition at monotonically lower pressures and reduced volumes with increasing degree of asphericity, in consistent agreement with data from computer simulation experiments. The results developed by the Boublík equations are compared with those of the simplified perturbed hard chain theory (SPHCT); and the SPHCT formalism is shown to give acceptably accurate results for the density and Gibbs free enthalpy at pressures less than approximately 50000 atm, and modest degrees of asphericity.

References

1. J. F. Kenney, Phys. Chem. Chem. Phys., 1999, 1, 3277.
2. N. F. Carnahan and K. E. Starling, J. Chem. Phys., 1969, 51, 635.
3. H. Reiss, H. L. Frisch and J. L. Lebowitz, J. Chem. Phys., 1959, 31, 369.
4. H. Reiss, in Advances in Chemical Physics, ed. I. Prigogine, Interscience, New York, 1965, vol. 9, pp. 1–84.
5. H. Reiss and D. M. Tully-Smith, J. Chem. Phys., 1971, 55, 1674.
6. H. Reiss, in Statistical Mechanics and Statistical Methods in Theory and Application, ed. U. Landman, Plenum, London, 1977, pp. 99–140.
7. T. Boublík, J. Chem. Phys., 1975, 63, 4084.
8. T. Kihara, Rev. Mod. Phys., 1953, 25, 831.
9. T. Kihara, Adv. Chem. Phys., 1963, 5, 147.
10. T. Kihara, J. Phys. Soc. Jpn., 1953, 8, 686.
11. R. M. Gibbons, Mol. Phys., 1969, 17, 81.
12. B. Barboy and W. M. Gelbart, J. Chem. Phys., 1979, 71, 3053.
13. B. Barboy and W. M. Gelbart, J. Stat. Mech., 1980, 22, 709.
14. B. Barboy and W. M. Gelbart, J. Stat. Mech., 1980, 22, 685.
15. T. Boublík, J. Chem. Phys., 1970, 53, 471.
16. T. Boublík, Mol. Phys., 1974, 27, 1415.
17. T. Boublík, I. Nezbeda and O. Trnka, Czech. J. Phys. B., 1976, 26, 1081.
18. J. Pavlicek, I. Nezbeda and T. Boublík, Czech. J. Phys., 1979, B29, 1061.
19. T. Boublík, Mol. Phys., 1981, 42, 209.
20. B. J. Alder, W. G. Hoover and D. A. Young, J. Chem. Phys., 1968, 49, 3688; B. J. Alder and T. E. Wainwright, J. Chem. Phys., 1957, 27, 1208–1209.
21. J. H. Vera and J. M. Prausnitz, Chem. Eng. J., 1972, 3, 113.
22. S. Beret and J. M. Prausnitz, AIChE. J., 1975, 21, 1123.
23. M. D. Donohue and J. M. Prausnitz, AIChE. J., 1978, 24, 849.
24. A. van Pelt, C. J. Peters and J. de Swaan Arons, Fluid Phase Equilib., 1992, 74, 67.
25. D. Frenkel and B. M. Mulder, Mol. Phys., 1985, 55, 1171.
26. P. Bolhuis and D. Frenkel, J. Chem. Phys., 1997, 106, 666.
27. M. P. Allen, G. T. Evans and D. Frenkel, Adv. Chem. Phys., 1993, 86, 1.
28. J. D. Vernal, Nature, 1959, 183, 141.
29. J. D. Bernal and J. Mason, Nature, 1960, 188, 910.
30. J. D. Bernal, K. R. Knight and I. Cherry, Nature, 1964, 202, 852.
31. J. D. Bernal, Proc. R. Soc. London, Ser. A, 1964, 280, 299.
32. J. D. Bernal and S. V. King, in Physics of Simple Liquids, ed. H. N. V. Temperley, J. S. Rowlinson and G. S. Rushbrooke, North-Holland, Amsterdam, 1968.
33. G. O. Jones and P. A. Walker, Proc. Phys. Soc. B., 1953, 69, 1348.
34. J. S. Rowlinson and F. L. Swinton, Liquid and Liquid Mixtures, Butterworth, London, 1982.
35. H. Reiss and A. D. Hammerich, J. Chem. Phys., 1986, 90, 6252.
36. J. F. Kenney, Fluid Phase Equilib., 1998, 148, 21.