Analytical accurate expressions for radial distribution function and equation of state of hard sphere fluid based on the Percus-Yevick exact solution and a new unifying closure

ABSTRACT

New accurate analytic expressions for the radial distribution function and equation of state of hard sphere fluid are obtained by use of its analytic solution from Percus-Yevick closure and by a new unifying closure of the Ornstein-Zernike integral equation. This will be possible by linearisation of the closure to get a set of one-parameter structural functions incorporating both Percus-Yevick and Hyper-Netted Chain closures. This will enable us to deliver very general expressions for the structural functions and equation of state for a potential and fluid. For the most important case of hard sphere fluid the method can be complemented with its known virial coefficients to get accurate analytical expressions for its radial distribution function and equation of state. The expressions are then successfully compared with those of computer simulations for hard sphere fluid at all densities with great accuracy.

KEYWORDS:

• One-Parameter integral equation
• hard sphere fluid
• liquid state theory

Acknowledgements

I would like to thank the Islamic Azad University, Amol Branch for generous financial support of the research project.

Disclosure statement

No potential conflict of interest was reported by the author(s).