Abstract
The diffusion coefficient and velocity autocorrelation function for a fluid of particles interacting through a square-well or square-shoulder potential are calculated from a kinetic theory similar to the Davis-Rice-Sengers theory and the results are compared to those of computer simulations. At low densities the theory yields too low estimates due to the neglect of correlations between subsequent partial collisions of identical pairs; in particular, the neglect of boundstate effects appears important. At intermediate densities the theory makes reasonable predictions and at high densities it produces too high values, due to the neglect of ring terms and other correlated collision events. The results for the square-shoulder potential generally exhibit better agreement between theory and simulations than do those for the square-well potential.
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References
B. J. Alder and T. E. Wainwright,Phys. Rev. Lett. 18:988 (1967).
D. Enskog,K. Sven. Vetenskapsakad. Handl. 63:4 (1922).
H. van Beijeren and M. H. Ernst,Physica 68:437 (1973);70:225 (1973).
W. E. Alley and B. J. Alder,Phys. Rev. A 27:3158 (1983); W. E. Alley, B. J. Alder, and S. Yip,Phys. Rev. A 27:3174 (1983); E. G. D. Cohen, B. Kamgar-Parsi, and I. M. de Schepper,Phys. Lett. 114A:241 (1986).
I. M. de Schepper, J. C. van Rijs, A. H. van Well, P. Verkerk, L. A. de Graaf, and C. Bruin,Phys. Rev. A 29:1602 (1984).
H. T. Davis, S. A. Rice, and J. V. Sengers,J. Chem. Phys. 35:2210 (1961).
J. Karkheck, H. van Beijeren, I. M. de Schepper, and G. Stell,Phys. Rev. A 32:2517 (1985).
E. H. Hauge, inTransport Phenomena, G. Kirczenow and J. Marro, eds. (Springer, Berlin), p. 337.
P. Résibois and M. de Leener,Classical Kinetic Theory of Fluids (Wiley, New York, 1977).
I. S. Gradshteyn and I. M. Ryzhik,Table of Integrals, Series and Products (Academic Press, New York, 1965).
H. Wilbertz, Diplomarbeit, RWTH Aachen (unpublished).
J. P. J. Michels and N. J. Trappeniers,Physica 116A:316 (1982).
A. J. Batschinsky,Z. Phys. Chem. 84:643 (1913); J. H. Hildebrand,Viscosity and Diffusivity (Wiley, New York, 1976).
J. J. van Loef,Physica 124B:305 (1984); P. S. van der Gulik and N. J. Trappeniers,Physica 135A:1 (1986).
J. P. J. Michels and N. J. Trappeniers,Physica 90A:179 (1978).
E. McLaughlin,Trans. Faraday Soc. 55:28 (1959); R. Zwanzig and M. Bixon,Phys. Rev. A 2:2005 (1970).
I. M. de Schepper, A. F. E. M. Haffmans, and H. van Beijeren,Phys. Rev. Lett. 57:1715 (1986).
J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird,Molecular Theory of Gases and Liquids (Wiley, New York, 1967).
M. C. Marchetti and J. W. Dufty,Chem. Phys. Lett. 70:539 (1980).
J. Karkheck and G. Stell,J. Phys. Chem. 87:2858 (1983).
Ya. G. Sinai,Introduction to Ergodic Theory (Princeton University Press, 1976).
I. M. de Schepper and E. G. D. Cohen,Phys. Lett. 68A:308 (1978); H. van Beijeren,Phys. Lett. 105A:191 (1984); T. R. Kirkpatrick,Phys. Rev. Lett. 53:1735, 2185 (1984).
J. J. Erpenbeck and W. W. Wood,Phys. Rev. A 32:412 (1985).
J. P. J. Michels and N. J. Trappeniers,Chem. Phys. Lett. 33:195 (1975); M. C. Marchetti and J. W. Dufty,Phys. Rev. A 24:2116 (1981).
S. Chapman and T. G. Cowling,The Mathematical Theory of Non-Uniform Gases (Cambridge University Press, Cambridge, 1960).
H. van Beijeren, J. Karkheck, and J. V. Sengers,Phys. Rev. A 37:2247 (1988).
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Wilbertz, H., Michels, J., van Beijeren, H. et al. Self-diffusion of particles interacting through a square-well or square-shoulder potential. J Stat Phys 53, 1155–1177 (1988). https://doi.org/10.1007/BF01023862
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DOI: https://doi.org/10.1007/BF01023862