Global and critical test of the perturbation density-functional theory based on extensive simulation of Lennard-Jones fluid near an interface and in confined systems

Free energy density functional for adsorption of fluids in nanopores

A classical free energy density functional, which is isomorphic to a usual effective hard sphere model + mean field approximation for tail contribution, is proposed for treatment of real fluids in inhomogeneous states. In the framework of the classical density functional theory (DFT), the present functional is applied to two representative model fluids, namely, a Lennard-Jones fluid and a hard core attractive Yukawa fluid, subject to influence of various external fields. A comprehensive comparison with simulation results and a detailed analysis show that the present functional holds simultaneously all of the desirable properties inherent in an excellent functional, such as high accuracy, computational simplicity, consistency with a hard wall sum rule, nonrecourse to use of adjustable parameter(s) and weighted densities, reproduction of bulk second-order direct correlation function (DCF) in bulk limit, and applicability to subcritical fluid phenomena.

Is perturbation DFT approach applicable to purely repulsive fluids?

A recently proposed third order + second order perturbation density functional theory (DFT) approach is tested for the validity and applicability to purely repulsive model fluids subjected to various external fields. Hard core repulsive Yukawa potential, point particle Yukawa potential, and inverse power potential are employed as sample models. Theoretical DFT results are compared with the corresponding simulation data obtained by grand canonical ensemble Monte Carlo simulation. This comparison indicates that the third order + second order perturbation DFT approach is suitable for these purely repulsive fluids only on condition of high accuracy of the imported bulk second order direct correlation function (DCF). However, in this case the origin of the successful performance somewhat differs from that observed for the mean field approximation applied to van der Waals fluids. In the present case it originates from the observation that the bulk second order DCF is strongly dependent on the density argument for the hard-core part, while for the distances exceeding the core dimension this dependence is considerably weaker.

How to extend hard sphere density functional approximation to nonuniform nonhard sphere fluids: Applicable to both subcritical and supercritical temperature regions

A methodology for the formulation of density functional approximation (DFA) for nonuniform nonhard sphere fluids is proposed by following the spirit of a partitioned density functional approximation [Zhou, Phys. Rev. E 68, 061201 (2003)] and mapping the hard core part onto an effective hard sphere whose high order part of the functional perturbation expansion is treated by existing hard sphere DFAs. The resultant density functional theory (DFT) formalism only needs a second order direct correlation function and pressure of the corresponding coexistence bulk fluid as inputs and therefore can be applicable to both supercritical and subcritical temperature cases. As an example, an adjustable parameter-free version of a recently proposed Lagrangian theorem-based DFA is imported into the present methodology; the resultant DFA is applied to Lennard-Jones fluid under the influence of external fields due to a single hard wall, two hard walls separated by a small distance, a large hard sphere, and a spherical cavity with a hard wall. By comparing theoretical predictions with previous simulation data and those recently supplied for coexistence bulk fluid situated at "dangerous" regions, it was found that the present DFA can predict subtle structure change of the density profile and therefore is the most accurate among all existing DFT approaches. A detailed discussion is given as to why so excellent DFA for nonhard sphere fluids can be drawn forth from the present methodology and how the present methodology differs from previous ones. The methodology can be universal, i.e., it can be combined with any other hard sphere DFAs to construct DFA for other nonhard sphere fluids with a repulsive core.

Further Test of Third Order + Second-Order Perturbation DFT Approach: Hard Core Repulsive Yukawa Fluid Subjected to Diverse External Fields

Grand canonical Monte Carlo simulation is used to investigate density profiles of hard-core repulsive Yukawa (HCRY) model fluid under the influence of various external fields and radial distribution function (RDF) of the bulk HCRY system. The aim of these extensive simulations is to provide exact data for purely repulsive interaction potential against which the validity of a third order + second-order perturbation DFT approach can be tested. It is found that a semiempirical parametrized bridge function due to Malijevsky and Labik performs very well for the RDF of the bulk HCRY fluid. Incorporation of a bulk second-order direct correlation function (DCF) of the HCRY fluid based on the Malijevsky-Labik bridge function into the third order + second-order perturbation DFT approach yields the resulting theoretical predictions for the density profiles of inhomogeneous HCRY fluid that are in a very good agreement with the simulation data, an exception being somewhat larger deviations appearing for the structure of the fluid around the center of a hard spherical cavity. Both theory and simulation predict layering transition and gas-liquid coexistence phenomena occurring with the HCRY model fluid under confined conditions. For the case of an inverse sixth-power repulsive potential under the influence of a flat stationary wall defined by an inverse twelfth-power repulsive potential, the present third order + second-order perturbation DFT approach is found to be superior to several existing weighted density approximations (WDA) and partitioned WDA.