An accurate analytical representation of the bridge function of hard spheres and a question of existence of a general closure to the Ornstein–Zernike equation

• Published in: Collection of Czechoslovak chemical communications Vol. 76; no. 1; pp. 51 - 64
• Main Authors: Francová, Magda, Malijevský, Anatol, Labík, Stanislav, Kolafa, Jiří
• Format: Journal Article
• Language: English
• Published: Prague Blackwell Publishing Ltd 2011
• Subjects: Accuracy; Chemistry; Integral equations; Mathematical models; Phase transitions; Spheres; Studies
• ISSN: 1212-6950; 1212-6950; 2192-6506
• DOI: 10.1135/cccc2010127

The bridge function of hard spheres is accurately calculated from computer simulation data on the pair distribution function via the inverted Ornstein–Zernike equation at reduced densities ρ* ≡ N σ 3 / V ranging from 0.2 to 1.02, i.e. from low densities through densities in a vicinity of the phase transition to crystal to densities of metastable fluid region. The data are used to propose an analytical representation of the bridge function as a function of the interparticle distance and density. They are further used to construct the so-called Duh– Haymet plot. It is demonstrated that a “general closure” to the Ornstein–Zernike equation in the form B ( r ) = f [γ( r )], where γ is the indirect (or series) correlation function, does not match the data. Nor does an extended closure B ( r ) = f [γ( r ),ρ*] even in the simplest case of the one component hard sphere fluid. A relative success of literature closures to the Ornstein–Zernike equation is discussed.