Perturbation Density Functional Theory for Density Profile of A Nonuniform and Uniform Hard Core Attractive Yukawa Model Fluid

Abstract

The nonuniform first-order direct correlation function (DCF) for a hard-core attractive Yukawa model fluid (HCAYMF) was expanded around bulk density and truncated at the lowest order. The truncation was made formally exact by applying the functional counterpart of Lagrangian theorem of the differential calculus to the functional expansion. To calculate the density profile of a nonuniform HCAYMF, the uniform secondorder DCF from the mean spherical approximation for HCAYMF was employed; the resulting density functional theory (DFT) was computationally simpler and quantitatively more accurate than the previous weighted density approximation (WDA) + functional perturbation expansion approximation (FPEA) DFT, which divided the interaction potential into a short-ranged hard-sphere-like part and a long-ranged interaction part and treated the former by the WDA and the latter by third-order FPEA. The present DFT also was employed to calculate the radial distribution function of bulk HCAYMF and bulk hard-sphere fluid; the calculated results were in good agreement with simulation data.

Structure of Inhomogeneous Attractive and Repulsive Hard-Core Yukawa Fluid: Grand Canonical Monte Carlo Simulation and Density Functional Theory Study

“…If we fix a sphere, then the external potential produced by the fixed sphere is given by If the density profile of other spheres around the fixed particle is calculated from the DFT, the radial distribution function g(r) can be obtained through Equation 23 has been applied to attractive and repulsive HCY fluids. Figure 10 depicts the predicted radial distribution functions for the attractive HCY fluid at reduced temperature T* ) 2.0 and reduced densities 25, we found that the present DFT gives a more accurate radial distribution function than Zhou's perturbation DFT 25 does. Furthermore, our DFT is simpler in calculation than that of Zhou because we avoid the determination of the parameter from the bulk pressure.…”

New Weighted Density Functional Theory Based on Perturbative Approach

“…It may be noted that this form of the weighted density has also been used by Zhou. 31,32 Clearly in the homogeneous limit of F(r) f F 0 , F j(r) reaches the bulk density F 0 irrespective of the value of the parameter λ. The final equation for the first-order DCF c (1) -(r;[F]) of eq 5 is thus given by…”

Response behavior of diblock copolymer brushes in explicit solvent

“…and n α are the weighted densities (or fundamental measures). For the attraction term, some non-mean-field methods including the weighted density approximation [35][36][37] and quadratic density expansion 38,39 have been shown to be more accurate for simple fluids and have been successfully applied to several inhomogeneous systems such as square-well fluids, 40 Lennard-Jones fluids, 41 Yukawa potentials, 42,43 and Sutherland fluids. 44 However, these methods have not yet been extended to the polymer brush system.…”