Simple analytic equations of state for Sutherland fluids and square-well fluids

A simple analytic expression satisfying the limitation condition at low density for the radial distribution function of hard spheres is developed in terms of a polynomial expansion of nonlinear base functions and the Carnahan-Starling equation of state. The simplicity and precision for the expression is superior to the well-known Percus-Yevick expression. The coefficients contained in the expression were determined by fitting the Monte-Carlo data for the first coordination shell, and by fitting both the Monte-Carlo data and the numerical results of the Percus-Yevick expression for the second coordination shell. The expression has been applied to develop analytic equations of state for Sutherland fluids and square-well fluids. The numerical results are in good agreement with computer-simulation data.