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Ornstein–Zernike equation
About: Ornstein–Zernike equation is a research topic. Over the lifetime, 588 publications have been published within this topic receiving 26785 citations.
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01 Jan 1976
TL;DR: In this article, the authors present a mathematical model for time-dependent correlation functions and response functions in liquid solvers, based on statistical mechanics and molecular distribution functions, and show that these functions are related to time correlation functions in Ionic and Ionic liquids.
Abstract: Introduction. Statistical Mechanics and Molecular Distribution Functions. Computer "Experiments" on Liquids. Diagrammatic Expansions. Distribution Function Theories. Perturbation Theories. Time-dependent Correlation Functions and Response Functions. Hydrodynamics And Transport Coefficients. Microscopic Theories of Time-Correlation Functions. Ionic Liquids. Simple Liquid Metals. Molecular Liquids. Appendices. References. Index.
9,144 citations
TL;DR: In this paper, the three-dimensional classical many-body system is approximated by the use of collective coordinates, through the assumed knowledge of two-body correlation functions, and a self-consistent formulation is available for determining the correlation function.
Abstract: The three-dimensional classical many-body system is approximated by the use of collective coordinates, through the assumed knowledge of two-body correlation functions. The resulting approximate statistical state is used to obtain the two-body correlation function. Thus, a self-consistent formulation is available for determining the correlation function. Then, the self-consistent integral equation is solved in virial expansion, and the thermodynamic quantities of the system thereby ascertained. The first three virial coefficients are exactly reproduced, while the fourth is nearly correct, as evidenced by numerical results for the case of hard spheres.
2,358 citations
954 citations
TL;DR: 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.
436 citations
TL;DR: In this paper, an invariant expansion of the two-body statistical correlation function of a fluid is proposed, which does not depend on any particular reference frame used to define the orientation of the molecules and therefore can be reduced to the expansions of the literature in a simple way.
Abstract: An invariant expansion of the two‐body statistical correlation function of a fluid is proposed. This expansion does not depend on any particular reference frame used to define the orientation of the molecules, and therefore can be reduced to the expansions of the literature in a simple way. The new expansion permits a rather convenient way of including the effects of molecular symmetry into it. The expressions for a few thermodynamic properties in terms of this expansion are obtained. The equations for x‐ray, neutron, and light scattering are somewhat simpler using this expansion. The Ornstein—Zernike equation has a very convenient form, and is given in Fourier transformed form in terms of 6j angular recoupling coefficients.
400 citations