Structure of the square-shoulder fluid

Abstract

The structural properties of square-shoulder fluids are derived from the use of the rational function approximation method. The computation of both the radial distribution function and the static structure factor involves mostly analytical steps, requiring only the numerical solution of a single transcendental equation. The comparison with available simulation data and with numerical solutions of the Percus–Yevick and hypernetted-chain integral equations shows that the present approximation represents an improvement over the Percus–Yevick theory for this system and a reasonable compromise between accuracy and simplicity.

Keywords:

• radial distribution function
• square-shoulder potential
• rational function approximation
• Percus–Yevick integral equation
• hypernetted-chain integral equation

Acknowledgements

We want to thank C.N. Likos, J.R. Solana and R. Castañeda-Priego for sending us their simulation data. Two of us (S.B.Y. and A.S.) acknowledge the financial support of the Ministerio de Ciencia e Innovación (Spain) through Grant No. FIS2010-16587 (partially financed by FEDER funds) and of the Junta de Extremadura through Grant No. GR10158. The work of M.L.H. has been partially supported by DGAPA-UNAM under project IN-107010-2. He also wants to thank the hospitality of Universidad de Extremadura, where the first stages of this work were carried out.

Notes

Note

1. The numerical solutions were obtained by solving the system of algebraic equations resulting from the discretization of the integral equation. The convergence of the solutions was found to be acceptable for a grid size of Δr = 0.0125 and a cut-off distance .