Augmented Kierlik--Rosinberg Fundamental Measure Functional and Extension of Fundamental Measure Functional to Inhomogeneous Non-hard Sphere Fluids

摘要

From point of view of weighted density procedure, it is guessed that a Percus-Yevick (PY) compressibilityexcess free energy density, appearing in the Kierlik-Rosinberg type fundamental measure functional (KR-FMF) andexpressed in terms of scaled particle variables, can be substituted by a corresponding expression dictated by a moreaccurate Mansoori-Carnahan-Starling-Leland (MCSL) equation of state, while retaining the original weighting functions;it is numerically indicated that the resultant undesirable non-self-consistency between the PY type weighting functionand MCSL type excess free energy density had no bad effect on the performance of the resultant augmented KR-FMFwhich, on the one hand, preserves the exact low-density limit of the original KR-FMF and holds a high degree of pressureself-consistency, on the other hand, improves significantly, as expected, the predictions of density profile of hard spherefluid at single hard wall contact location and its vicinity, and of the bulk hard sphere second order direct correlationfunction (DCF), obtained from functional differentiation.The FMF is made applicable to inhomogeneous non-hardsphere fluids by supplementing a functional perturbation expansion approximation truncated at the lowest order withsummation of higher order terms beyond the lowest term calculated by the FMF for an effective hard sphere fluid;the resultant extended FMF only needs second order DCF and pressure of the fluid considered at coexistence state asinputs, consequently is applicable whether the considered temperature is above critical point or below critical point.The extended MCSL-augmented KR-FMF is found to be endowed with an excellent performance for predictions ofdensity profile and surface tension by comparing the present predictions of these two quantities with available computersimulation data for inhomogeneous hard core attractive Yukawa fluid and Lennard-Jones fluid.