Abstract
The Ornstein-Zernike (OZ) equation is considered for the wall-particle distribution functiong 0(x) in the case of a flat, impenetrable wall atx = 0 and a fluid of hard-core particles whose centers are constrained by the wall to occupy the semiinfinite spacex >σ/2, whereσ is the particle diameter. A solution is given in terms of the wall-particle direct correlation function c0(x) forx >σ/2, the bulk-fluid direct correlation function cB (t), and pB, the average bulk density. Explicit formulas for the contact surface density, total excess surface density, and the Laplace transform of the fluid density near the wall are given. For mean spherical type approximations, c0 (x) forx >σ/2 and cB (t) are both prescribed functions; for this case, a closed-form solution is obtained. An example is discussed and additional equations that enable one to go beyond the approximations considered above are introduced.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. Henderson, F. F. Abraham, and J. A. Barker, IBM Research Report #RJ 1690, December 1975; andMol. Phys. 31:1291 (1976).
J. K. Percus, Lecture Notes on Non-Uniform Fluids (Enseignement du 3ème Cycle de Physique en Suesse Romande, Eté 1975);J. Stat. Phys. 15:423 (1976).
E. Waisman, D. Henderson, and J. L. Lebowitz, to be published.
J. L. Lebowitz and J. K. Percus,Phys. Rev. 144:251 (1966).
J. S. Høye, J. L. Lebowitz, and G. Stell,J. Chem. Phys. 61:3252 (1974).
J. K. Percus and G. J. Yevick,Phys. Rev. 110:1 (1958); J. M. J. van Leeuwen, J. Groeneveld, and J. de Boer,Physica 25:792 (1959); T. Morita and K. Hiroike,Progr. Theor. Phys. (Kyoto) 23:1003 (1960); G. Stell, Fluids with Long Range Forces, inModern Theoretical Chemistry, Vol. IV,Statistical Mechanics, B. J. Berne, ed. (Plenum Press, New York, 1976).
R. J. Baxter,J. Chem. Phys. 52:4559 (1970); L. Blum,Mol. Phys. 30:1529 (1975); L. Blum,J. Chem. Phys. 61:2129 (1974).
R. J. Baxter,Aust. J. Phys. 21:563 (1968).
J. D. Jackson,Classical Electrodynamics (Wiley, New York, 1962).
J. R. Grigera and L. Blum,Chem. Phys. Lett. 38:486 (1976).
H. C. Andersen, D. Chandler, and J. D. Weeks,J. Chem. Phys. 57:2626 (1972).
G. Stell,Physica 29:517 (1963).
G. Stell,Phys. Rev. Lett. 20:533 (1968);Phys. Rev. B 1:2265 (1970).
J. L. Lebowitz and J. K. Percus,J. Math. Phys. 4:116, 248 (1963).
Author information
Authors and Affiliations
Additional information
Report #270, February 1976.
The observation of this paper that the wall-particle problem can be treated using standard Wiener-Hopf techniques was independently made by Percus in his work, which came to our attention too late to be compared to, or incorporated into, our own results here.
Rights and permissions
About this article
Cite this article
Blum, L., Stell, G. Solution of Ornstein-Zernike equation for wall-particle distribution function. J Stat Phys 15, 439–449 (1976). https://doi.org/10.1007/BF01020798
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01020798