International Journal of Thermophysics

, Volume 15, Issue 6, pp 1057–1072 | Cite as

Molecular simulation of phase coexistence: Finite-size effects and determination of critical parameters for two- and three-dimensional Lennard-Jones fluids

  • A. Z. Panagiotopoulos


The subject of this paper is the investigation of finite-size effects and the determination of critical parameters for a class of truncated Lennard-Jones potentials. Despite significant recent progress in our ability to model phase equilibria in multicomponent mixtures from direct molecular simulations, the accurate determination of critical parameters remains a difficult problem. Gibbs ensemble Monte Carlo simulations with systems of controlled linear system size are used to obtain the phase behavior in the near-critical region for two- and three dimensional Lennard-Jones fluids with reduced cutoff radii of 3, 3.5, and 5. For the two-dimensional systems, crossover of the effective exponent for the width of the coexistence curve from mean field (β = 1/2 in the immediate vicinity of the critical point to Ising-like (β= 1/8) farther away is observed. Critical parameters determined by fitting the data that follow Ising-like behavior are in good agreement with literature values obtained with finite-size scaling methods. For the three-dimensional systems, no crossover to mean field-type behavior was apparent. Extrapolated results for the critical parameters are consistent with literature estimates for similar fluids. For both two- and three-dimensional fluids, system size effects on the coexistence curves away from the critical point are small, normally within simulation statistical uncertainties.

Key words

critical exponents critical point critical temperature finite size effects Gibbs ensemble Lennard-Jones Monte Carlo simulation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Z. Panagiotopoulos,Mol. Phys. 62:701 (1987); A. Z. Panagiotopoulos, N. Quirke, M. Stapleton, and D. J. Tildesley,Mol. Phys. 63:527 (1988).Google Scholar
  2. 2.
    B. Smit, Ph. De Smedt, and D. Frenkel,Mol. Phys. 68:931 (1989); B. Smit and D. Frenkel,Mol. Phys. 68:951 (1989).Google Scholar
  3. 3.
    D. Frenkel and A. J. C. Ladd,J. Chem. Phys. 81:3188 (1984).Google Scholar
  4. 4.
    A. Z. Panagiotopoulos,Int. J. Thermophys. 10:447 (1989).Google Scholar
  5. 5.
    An introduction to finite-size scaling and the extensive literature on the subject is given in Section 2.3 of K. Binder and D. W. Heermann,Monte Carlo Simulation in Statistical Physics, 2nd ed., Solid-State Sciences Vol. 80 (Springer-Verlag, Berlin, 1993).Google Scholar
  6. 6.
    M. Rovere, P. Nielaba, and K. Binder,Z. Phys. 90:215 (1993).Google Scholar
  7. 7.
    N. B. Wilding and A. D. Bruce,J. Phys. Condens. Matter 4:3087 (1992); A. D. Bruce and N. B. Wilding,Phys. Rev. Lett. 68:193 (1992).Google Scholar
  8. 8.
    K. K. Mon and K. Binder,J. Chem. Phys. 96:6989 (1992).Google Scholar
  9. 9.
    J. R. Recht and A. Z. Panagiotopoulos,Mol. Phys. 80:843 (1993).Google Scholar
  10. 10.
    D. G. Green, G. Jackson, E. de Miguel, and L. F. Rull,J. Chem. Phys. 101:3190 (1994).Google Scholar
  11. 11.
    B. Smit and D. Frenkel,J. Chem. Phys. 94:5663 (1991).Google Scholar
  12. 12.
    L. Vega, E. de Miguel, L. F. Rull, G. Jackson, and I. A. McLure,J. Chem. Phys. 96:2296 (1992).Google Scholar
  13. 13.
    J. M. Yeomans,Statistical Afechanics the Phase Transitions (Oxford University Press, Oxford, 1992).Google Scholar
  14. 14.
    A. Z. Panagiotopoulos,Mol. Simul. 9:1 (1992).Google Scholar
  15. 15.
    B. Smit and D. Frenkel,J. Phys. Condens. Matter 1:8659 (1989).Google Scholar
  16. 16.
    J. S. Rowlinson and F. L. Swinton,Liquids and Liquid Mixtures, 3rd ed. (Butterworths, London, 1982 ).Google Scholar
  17. 17.
    R. R. Singh, K. S. Pitzer, J. J. de Pablo, and J. M. Prausnitz,J. Chem. Phys. 92:5463 (1990).Google Scholar
  18. 18.
    B. Smit,J. Chem. Phys. 96:8639 (1992).Google Scholar
  19. 19.
    A. Lotfi, J. Vrabec, and J. Fischer,J. Mol. Phys. 76:1319 (1992).Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • A. Z. Panagiotopoulos
    • 1
  1. 1.School of Chemical EngineeringCornell UniversityIthacaUSA

Personalised recommendations