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Journal ArticleDOI

Ornstein–Zernike Relation and Percus–Yevick Approximation for Fluid Mixtures

01 May 1970-Journal of Chemical Physics (American Institute of Physics)-Vol. 52, Iss: 9, pp 4559-4562
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.
Citations
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Journal ArticleDOI
TL;DR: In this article, the authors derived expressions for changes in the thermodynamic properties due to association in mixtures of molecules with multiple bonding sites, where the equations are written in terms of a hard-core reference whose pair distribution function is known.
Abstract: As a continuation of our work on spherical associating molecules, we have derived expressions for changes in the thermodynamic properties due to association in mixtures of molecules with multiple bonding sites. The equations are written in terms of a hard-core reference whose pair distribution function is known. In practise, the hard-sphere reference mixture is the easiest to use. A reference system of homonuclear chains is examined in order to account for asymmetries in molecular shape; chains are constructed by bonding equal-sized spheres together. An equation of state for hard-sphere chains is obtained which is in good agreement with recent simulation data. Expressions for mixtures of homonuclear chains of different sizes are also presented. The approach is extended to examine associating chain molecules with multiple bonding sites. The phase equilibria of non-associating chains, and of associating chains with one or two bonding sites are determined. In this study, the separate effects of molecular ass...

1,115 citations

Journal ArticleDOI
TL;DR: In this article, the authors present a review of recently achieved progress in the field of soft condensed matter physics, and in particular on the study of the static properties of solutions or suspensions of colloidal particles.

1,056 citations

Journal ArticleDOI
TL;DR: In this paper, the effect of molecular associations on the phase coexistence properties of hard-sphere fluids with one or two directional, attractive centers is investigated and the critical points and phase equilibria of the associating fluids are determined for various values of the strength and range of the attractive site.
Abstract: The effect of molecular associations on the phase coexistence properties of fluids with one or two directional, attractive centres is investigated. The individual molecules are represented by hard-sphere repulsive cores with off-centre, square-well attractive sites. Such a system’s thermodynamic properties can be calculated by using expressions based on a theory recently proposed by Wertheim. Isothermal-isobaric Monte Carlo simulations of hard-sphere fluids with one or two attractive sites are shown to be in good agreement with the results of the theory. In order to study the system’s phase equilibria using the theory, a simple van der Waals mean-field term is added to account for the dispersion forces. The critical points and phase equilibria of the associating fluids are determined for various values of the strength and range of the attractive site. Furthermore, results are presented for the degree of association in the gas and liquid phases along the vapour pressure curve. The theory can treat fluids with strong hydrogen-bonding associations such as those found in the carboxylic acids, the aliphatic alcohols, hydrogen fluoride, water etc.

724 citations

Journal ArticleDOI
TL;DR: In this paper, the mean spherical approximation for the primitive model of electrolytic solutions is solved for the most general case of an arbitrary charge and size, and the excess thermodynamic properties are scaled to the charge and the size by means of a rational expression involving a single parameter.
Abstract: The mean spherical approximation for the primitive model of electrolytic solutions is solved for the most general case of an arbitrary charge and size. It is found that the excess thermodynamic properties are scaled to the charge and the size by means of a rational expression involving a single parameter. This parameter is found by solving an algebraic equation. The explicit form of this equation is obtained for the cases of a binary mixture and in the limit of low concentrations.

706 citations

Journal ArticleDOI
TL;DR: For a survey of the current knowledge of the dynamics and statics of charge-stabilized suspensions in the fluid phase, with emphasis on the authors own work, see.

360 citations

References
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Journal ArticleDOI
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.
Abstract: We have investigated the thermodynamic properties of a binary mixture of hard spheres (with special reference to the existence of a phase transition) by using the recently obtained exact solution of the generalized equations of Percus and Yevick for the radial distribution functions of such a mixture. The distribution function obtained from the equations of Percus and Yevick is only an approximation and so yields two different pressures, pc and pv, when used, respectively, in the compressibility equation of Ornstein and Zernike and in the equation of state obtained from the virial theorem. Comparisons with machine calculations show that pc is slightly above and pv slightly below the true pressure but that both are close to it. Our results show that the volume change on mixing at constant pressure is negative at all densities and compositions within the fluid phase when it is calculated from pc, but that it becomes positive at high densities when calculated from pv. In neither case is there a separation in...

354 citations

Journal ArticleDOI
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.
Abstract: 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.B.G.K.Y.) approximation or the hypernettedchain approximation. It is noted that the reason for this finding lies in the fact that the Percus and Yevick approximation chooses a quite advantageous function for making a Taylor expansion of the appropriate equation for a grand canonical ensemble. (T.F.H.)

310 citations

Journal ArticleDOI
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.
Abstract: The Ornstein–Zernike equation for a homogeneous fluid relates the direct correlation function c(r) and the indirect correlation function h(r). In this paper it is shown that if c(r) vanishes beyond a range R then a third function Q(r) can be introduced which is related to c(r) and h(r) by equations that involve the functions only over the range (O,R). The analytic solution of the Percus–Yevick approximation for hard spheres can then be obtained very simply and, as c® normally tends rapidly to zero with increasing r, it is expected that the results should be of use in numerical calculations based on the Percus–Yevick, convolution-hypernetted chain, or similar approximations.

301 citations

Journal ArticleDOI
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.
Abstract: An exact integral equation is found for the pair distribution function. The integral equation is of somewhat different nature from the usual ones known in the theory of classical fluids, in the point that it involves an infinite series. The Helmholtz free energy is expressed as a series expansion which may be more rapidly convergent than the usual one. It is shown that the integral equation can be derived also by means of a variational principle from the expression for the free energy. It is pointed out that the theory of classical fluids may be constructed with the knowledge of the pair distribution function alone, even if a form of the pair interaction potential is not known.

298 citations

Journal ArticleDOI
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.
Abstract: An efficient method of solving the Percus‐Yevick and related equations is described. The method is applied to a Lennard‐Jones fluid, and the solutions obtained are discussed. It is shown that the Percus‐Yevick equation predicts a phase change with critical density close to 0.27 and with a critical temperature which is dependent upon the range at which the Lennard‐Jones potential is truncated. At the phase change the compressibility becomes infinite although the virial equation of state does not show this behavior. Outside the critical region the PY equation is at least two‐valued for all densities in the range (0, 0.6).

70 citations