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Thermodynamic perturbation theory of simple liquids: Monte Carlo simulation of a hard sphere system and the Helmholtz free energy of SW fluids

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Abstract

The Monte Carlo method is used to simulate similar sized hard sphere systems in a wide range of densities (from η 0.005 to 0.530 with a step of η = 0.005). The models are used to calculate the coefficients of the thermodynamic perturbation theory series for SW fluids up to the fourth order. The width of the attraction zone of the SW potential λ is varied from 1 to 2.5 sphere diameters. The analytical expressions approximating the obtained coefficients by polynomials with respect to the variables η and λ are determined. The absolute accuracy of the approximation is estimated to be better than ±0.001. All the necessary data for the calculation of the Helmholtz free energy of SW fluids up to the fourth-order perturbation theory are given.

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References

  1. B. J. Alder, D. A. Young, and M. A. Mark, J. Chem. Phys., 56, No. 6, 3013–3029 (1972).

    Article  CAS  Google Scholar 

  2. D. Henderson, W. G. Madden, and D. D. Fitts, J. Chem. Phys., 64, No. 12, 5026–5034 (1976).

    Article  CAS  Google Scholar 

  3. D. Henderson, O. H. Scalise, and W. R. Smith, J. Chem. Phys., 72, No. 4, 2431–2437 (1980).

    Article  CAS  Google Scholar 

  4. L. Vega, S. A. Safran, S. A. Kim, and G. S. Grest, J. Chem. Phys., 96, No. 3, 2296–2305 (1992).

    Article  CAS  Google Scholar 

  5. J. R. Elliott and L. Hu, J. Chem. Phys., 110, No. 6, 3043–3048 (1999).

    Article  CAS  Google Scholar 

  6. J. Largo and J. R. Solana, J. Phys. Chem. B, 108, 10062–10070 (2004).

    Article  CAS  Google Scholar 

  7. J. A. Barker and D. Henderson, J. Chem. Phys., 47, No. 8, 2856–2861 (1967).

    Article  CAS  Google Scholar 

  8. J. A. Barker and D. Henderson, J. Chem. Phys., 47, No. 11, 4714–4720 (1967).

    Article  CAS  Google Scholar 

  9. S. B. Yuste and A. Santos, J. Chem. Phys., 101, No. 3, 2355–2364 (1994).

    Article  CAS  Google Scholar 

  10. L. Acedo and A. Santos, J. Chem. Phys., 115, No. 6, 2805–2817 (2001).

    Article  CAS  Google Scholar 

  11. W. R. Smith, D. Henderson, and J. A. Barker, J. Chem. Phys., 55, No. 8, 4027–4033 (1971).

    Article  CAS  Google Scholar 

  12. J. Largo, J. R. Solana, L. Acedo, and A. Santos, Mol. Phys., 101, No. 19, 2981–2986 (2003).

    Article  CAS  Google Scholar 

  13. A. Diez, J. Largo, and J. R. Solana, J. Chem. Phys., 125, 074509 (2006).

    Article  CAS  Google Scholar 

  14. J. Largo and J. R. Solana, Mol. Simul., 29, 363–371 (2003).

    Article  CAS  Google Scholar 

  15. J. Largo, J. R. Solana, S. B. Yuste, and A. Santos, J. Chem. Phys., 122, 084510 (2005).

    Article  CAS  Google Scholar 

  16. Yu. T. Pavlyukhin, J. Struct. Chem., 47, Supplement, S173–S190 (2006).

    Article  CAS  Google Scholar 

  17. J. A. Barker and D. Henderson, Rev. Mod. Phys., 48, No. 4, 587–673 (1976).

    Article  CAS  Google Scholar 

  18. R. W. Zwanzig, J. Chem. Phys., 22, No. 8, 1420–1426 (1954).

    Article  CAS  Google Scholar 

  19. Yu. T. Pavlyukhin, J. Struct. Chem., 50, No. 3, 446–455 (2009).

    Article  CAS  Google Scholar 

  20. L. D. Landau and E. M. Lifshits, Statistical Physics [in Russian], Part 1, 3rd ed., Nauka, Moscow (1976).

    Google Scholar 

  21. H. N. V. Temperley, J. S. Rowlinson, and G. S. Rushbrooke (eds.), in: Physics of Simple Liquids, North-Holland, Amsterdam (1968).

    Google Scholar 

  22. J. D. Weeks, D. Chandler, and H. C. Andersen, J. Chem. Phys., 30, No. 12, 5237–5247 (1971).

    Article  Google Scholar 

  23. H. C. Andersen, J. D. Weeks, and D. Chandler, Phys. Rev A, 4, No. 4, 1597–1607 (1971).

    Article  Google Scholar 

  24. L. Verlet and J.-J. Weis, Phys. Rev. A, 5, No. 2, 939–952 (1972).

    Article  Google Scholar 

  25. F. H. Ree, J. Chem. Phys., 64, No. 11, 4601–4605 (1976).

    Article  CAS  Google Scholar 

  26. M. Ross, J. Chem. Phys., 71, No. 4, 1567–1571 (1979).

    Article  CAS  Google Scholar 

  27. F. Lado, Mol. Phys., 52, No. 4, 871–876 (1984).

    Article  CAS  Google Scholar 

  28. H. G. Kang, S. C. Lee, and T. Ree, J. Chem. Phys., 82, No. 1, 415–423 (1985).

    Article  Google Scholar 

  29. R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics, Wiley, New York (1975).

    Google Scholar 

  30. C. A. Croxton, Liquid State Physics — A Statistical Mechanical Introduction, Cambridge University Press, (1974).

  31. A. Mulero, C. Galan, and F. Cuadros, Phys. Chem. Chem. Phys., 3, 4991–4999 (2001).

    Article  CAS  Google Scholar 

  32. Yu. T. Pavlyukhin, J. Struct. Chem., 49, No. 5, 944–949 (2008).

    Article  CAS  Google Scholar 

  33. http:www.solid.nsc.ru/SCIENTISTS/PAVLUKHIN/PAPERS/default.htm#iii

  34. Yu. T. Pavlyukhin, J. Struct. Chem., 48, No. 6, 1073–1081 (2007).

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Institute of Solid State Chemistry and Mechanochemistry, Siberian Division, Russian Academy of Sciences, Novosibirsk, Russia

    Yu. T. Pavlyukhin

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  1. Yu. T. Pavlyukhin
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Correspondence to Yu. T. Pavlyukhin.

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Original Russian Text Copyright © 2012 by Yu. T. Pavlyukhin

__________

Translated from Zhurnal Strukturnoi Khimii, Vol. 53, No. 3, pp. 482–492, May–June, 2012.

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Pavlyukhin, Y.T. Thermodynamic perturbation theory of simple liquids: Monte Carlo simulation of a hard sphere system and the Helmholtz free energy of SW fluids. J Struct Chem 53, 476–486 (2012). https://doi.org/10.1134/S0022476612030092

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  • DOI: https://doi.org/10.1134/S0022476612030092

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