A double Yukawa potential for the van der Waals interaction of molecules: application to a determination of the critical temperature

Abstract

A double Yukawa (DY) potential, fitted on the carbon - carbon (CC) van der Waals (vdW) Lennard-Jones 12,6 (LJ) potential and integrated on two facing spheres, yields another DY function, whose parameters are simply related to those of the original CC LJ. We exploit this fact to obtain a new analytic expression of the DY type that describes the high-temperature physical interactions between molecules in good agreement with the well-known Girifalco potential, which was obtained from the direct spherical integration of the LJ potential. The main advantage of having a DY pair potential comes from the fact that analytic expressions of thermodynamic functions can be obtained within the Percus - Yevick approximation of the Ornstein - Zernike equation. As an example, an analytic expression of the Helmholz free energy is derived, and the double tangent construction on its vdW loop allows the determination of the liquid - vapour coexistence line and an estimation of the critical parameters ( K, ). This is in good agreement with the results predicted from various other theories with the Girifalco potential.