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A general solution of the molecular Ornstein–Zernike equation for spheres with anisotropic adhesion and electric multipoles (1990)

Blum, L. ; Cummings, P. T. ; Bratko, D.

College Park, Md. : American Institute of Physics (AIP)

The Journal of Chemical Physics 92 (1990), S. 3741-3747

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ISSN: 1089-7690

Source: AIP Digital Archive

Topics: Physics , Chemistry and Pharmacology

Notes: We present the analytic solution of the molecular Ornstein–Zernike equation for a very general closure in which the direct correlation function is of the form suggested by the mean-spherical approximation for arbitrary multipolar interactions and the total correlation function contains terms that arise in the Percus–Yevick approximation for spheres with anisotropic surface adhesion. In addition to generalizing several earlier analyses of special cases of this closure, the solution presented here contains new simplifying insights that reduce the complexity of the resulting algebraic equations. A special case of the analysis is described to illustrate the method of solution.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1063/1.457832

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A new method for the numerical solution of integral equation approximations (1990)

Cummings, P. T. ; Monson, P. A.

Springer

International journal of thermophysics 11 (1990), S. 97-107

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ISSN: 1572-9567

Keywords: critical phenomena ; integral equation approximations ; numerical methods ; Ornstein-Zernike equation

Source: Springer Online Journal Archives 1860-2000

Topics: Physics

Notes: Abstract A new numerical technique for solving the Ornstein-Zernike equation is described. It is particularly useful in solving the Ornstein-Zernike equation for approximations and pair potentials (such as the Percus-Yevick and mean spherical approximations for finite ranged potentials) which imply a finiteranged direct correlation function since for such approximations the numerical technique is essentially exact. The only approximation involved in such cases is the discretization of direct and total correlation functions over the finite range on which the direct correlation function is nonzero. Thus, the new method avoids truncation of the total correlation function and should permit the critical point and spinodal curve to be mapped out with greater accuracy than is permitted by existing methods. Preliminary explorations on the stability and accuracy of the method are described.