A new simple analytical expression for the average site–site radial distribution function of hard sphere chain fluid

A new simple analytical expression for the first coordination shell (1 ≤ x ≤ 2) of the average site–site intermolecular radial distribution function (ASSIRDF) of freely jointed tangent hard sphere chain fluid (FJTHSC) is proposed. The proposed expression is a polynomial expansion of packing fraction. The dependence of each polynomial coefficient on the radial coordinate and segment number is described by a polynomial expansion of nonlinear base function and a simple relation proposed by Liu and Hu, respectively. The coefficients involved in the expression of ASSIRDF are optimized by fitting the numerical values of Percus–Yevick (PY) integral equation theory of Chiew. The proposed expression of ASSIRDF is applied to an analytical perturbative equation of state (EOS) in order to modify it and improve its accuracy in predicting the compressibility factor and vapor–liquid equilibria of freely jointed tangent square-well chain (FJTSWC) fluids of variable well-widths (1 ≤ λ ≤ 2). The predicted results are in good agreement with the simulation data and also compared with that of other well-known equations of state.

► A new simple analytical expression for the ASSIRDF of FJTHSC fluid.
► Vapor-liquid equilibria and compressibility factor of FJTSWC fluid.
► Fitting the numerical values of PY integral equation theory of Chiew.