An integral equation for classical fluids at equilibrium

Abstract

A new integral equation for describing multicomponent classical molecular fluids at equilibrium is presented ; the derivation of this theory makes use of the functional Taylor expansion technique of Percus and the FourierWigner expansion. A diagrammatic analysis of the equation is developed and the theory is discussed. INTRODUCTIONThe structure and the thermodynamics of classical fluids at equilibrium have been investigated through theories using approximate integral equations, the reference [1] gives an excellent review of these theories. In particular, Chandler presented a derivation of the RISM equation [2], an integral equation for classical molecular fluids considered as fused hard spheres, and applied it for some non-trivial molecules. Topol and Claverie discussed the validity of this theory [14] and derived the equation of state for the same molecular model. Johnson presented an integral equation related to the RISM equation, that could handle any type of site-site pair interaction for classical molecular fluids [9]. Recently, the generalized Percus-Yevick (PY) and hypernetted chain (HNC) integral equations and closed expressions for the compressibility pressure have been derived rigorously for single and multicomponent classical molecular fluids [4][5][6][7][8].It is well-known that the PY approximation is 'suitable for short-range interactions and that the HNC approximation is better for long-range interactions [1]. By using these methods a new integral equation for multicomponent classical fluids is derived ; this theory combines the properties of the generalized PY and HNC theories.In w 2 we give some definitions. In w 3 the new integral equation is derived by using the functional Taylor expansion of Percus and the Fourier-Wigner expansion of the angular functions. In w 4 a diagrammatic analysis of the three integral equations is presented. Section 5 presents the conclusions.