On equivalence of high temperature series expansion and coupling parameter series expansion in thermodynamic perturbation theory of fluids

Abstract: The coupling parameter series expansion and the high temperature series expansion in the ther- modynamic perturbation theory of fluids are shown to be equivalent if the interaction potential is pairwise additive. As a consequence, for the class of fluids with the potential having a hardcore repulsion, if the hard-sphere fluid is chosen as reference system, the terms of coupling parameter series expansion for radial distribution function, direct correlation function and Helmholtz free energy follow a scaling law with temperature. The scaling law is confirmed by application to square-well fluids.