Journal ArticleDOI
Ornstein–Zernike Relation and Percus–Yevick Approximation for Fluid Mixtures
TLDR
In this paper, a transformation of the Ornstein-Zernike relation for fluid mixtures is derived which involves the direct and indirect correlation functions only over the ranges within which the former are nonzero.Abstract:
A transformation of the Ornstein–Zernike relation for fluid mixtures is derived which involves the direct and indirect correlation functions only over the ranges within which the former are nonzero. Also, two closed expressions for the compressibility pressure in the Percus–Yevick (PY) approximation for mixtures are presented. The analytic solution of the PY approximation for mixtures of hard spheres follows immediately, and it is expected that the results should be of use in numerical calculations for systems with short‐range forces, where the direct correlation functions normally tend rapidly to zero with increasing particle separation.read more
Citations
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Journal ArticleDOI
Solution of the Yukawa closure of the Ornstein-Zernike equation
J. S. Høye,L. Blum +1 more
TL;DR: In this article, the solution of the Ornstein-Zernike equation with Yukawa closure was generalized for an arbitrary number of Yukawas, using the Fourier transform technique introduced by Baxter, and full equivalence to the results of Waisman, Hoye, and Stell was proved for the case of a single Yukawa.
Journal ArticleDOI
Invariant expansion III: The general solution of the mean spherical model for neutral spheres with electostatic interactions
TL;DR: In this paper, the partial solution for the mean spherical model of neutral spheres with electrostatic interactions obtained in a previous communication is extended to the general case, in which the dipole-quadrupole interaction is included.
Journal ArticleDOI
Polydisperse systems. I. Scattering function for polydisperse fluids of hard or permeable spheres
TL;DR: In this article, the scattering function for a polydisperse fluid of hard spheres is given in the Percus-Yevick approximation for a simple model of interpenetrable particles introduced in order to widen the applicability of their results to colloid and polymer problems.
Journal ArticleDOI
A new interpretation of the sticky hard sphere model
TL;DR: In this paper, the basic results of the sticky hard sphere model were derived using a perturbative solution of the factorized form of the Ornstein-Zernike equation and the Percus-Yevick closure relation.
Journal ArticleDOI
Solution of a model for the solvent‐electrolyte interactions in the mean spherical approximation
TL;DR: In this article, an electrolytic solution is simulated by a mixture of charged hard spheres and hard dipoles, all of the same size, which can be solved exactly in the mean spherical approximation (MSA), yielding a set of three coupled high order algebraic equations for three unknowns, which are essentially the excess internal energies due to the charges alone, the dipoles alone, and the charge-dipole cross interaction.
References
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Journal ArticleDOI
Thermodynamic Properties of Mixtures of Hard Spheres
TL;DR: In this article, the authors investigated the thermodynamic properties of a binary mixture of hard spheres by using the recently obtained exact solution of the generalized equations of Percus and Yevick for the radial distribution functions of such a mixture.
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Approximation Methods in Classical Statistical Mechanics
TL;DR: In this paper, the pair distribution function for a classical fluid in thermal equilibrium is found to be more closely approximated by the Percus and Yevick (Phys. Rev., 110: 1(1958)) approximation than by the Bogoliubov-Born-Green- Kirkwood-Yvon (B.G.K.H.) approximation or the hypernetted chain approximation.
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Ornstein-Zernike relation for a disordered fluid
TL;DR: In this paper, it was shown that if the direct correlation function c(r) vanishes beyond a range R, then a third function Q(r), which is related to c and h (r) by equations that involve the functions only over the range (O,R), can be introduced.
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A New Approach to the Theory of Classical Fluids. I
Tohru Morita,Kazuo Hiroike +1 more
TL;DR: In this article, an exact integral equation for the pair distribution function is found for the Helmholtz free energy and the integral equation can be derived also by means of a variational principle from the expression for the free energy.
Journal ArticleDOI
Percus‐Yevick Equation Applied to a Lennard‐Jones Fluid
TL;DR: An efficient method of solving the Percus-Yevick and related equations is described in this paper, where the method is applied to a Lennard-Jones fluid, and the solutions obtained are discussed.