Density functional approximations for confined classical fluids

Yoon, Tai-Heui; Kim, Soon-Chul

doi:10.1103/physreve.58.4541

Cited by 30 publications

(20 citation statements)

References 30 publications

(2 reference statements)

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“…14 For the high temperature, the present formally exact second-order perturbative DFT shows a good agreement with the simulation data; the present predictions are even better than that of a previous weighted density approximation (WDA) + functional perturbative expansion approximation (FPEA) DFT, 9 which divided the interaction potential into a short-ranged hard-spherelike part and a long-ranged interaction part and treated the former by the computationally intensive WDA and the latter by the third-order FPEA, even if we did not display their results in the present figure for clarity. It is well-known that the previous WDA + FPEA + DFT is better than the modified version of the Lovett-Mou-Buff-Wertheim (LMBW-1) 14 for the predictions of the density distribution profile.…”

Section: Formally Exact Second-order Perturbation Density Functiosupporting

confidence: 79%

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

Zhou¹

2002

J. Phys. Chem. B

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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.

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Section: Formally Exact Second-order Perturbation Density Functiosupporting

confidence: 79%

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

Zhou¹

2002

J. Phys. Chem. B

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“…The agreement is very good with the most significant improvement over previous theories such as the singlet PY results [40,41] or the DFT by Choudhury and Ghosh [30] occurring in the density profiles close to contact with the wall. This reflects the property that the FMT complies with the contact theorem [42], while other DFTs need an adjustable parameter to obtain the correct contact value [32,33]. The results for the solvation force between two planar plates are also significantly better than the ones obtained with previous theories [33,40].…”

Section: Discussionmentioning

confidence: 76%

“…The quality of the FMT results is clearly superior to the results obtained from the OZ equation based PY singlet approximation [40,41] or the DFT by Choudhury and Ghosh [30], both of which deviate significantly from simulations especially close to contact with the wall. Higher order DFTs [31][32][33] require a fitting parameter in order to match the correct contact value or equation of state. In contrast, the fact that the FMT respects the contact theorem [42], i.e.…”

Section: Density Profilesmentioning

confidence: 99%

“…Expanding the one-particle DCF to quadratic order requires a formula for the unknown three-particle DCF c (3) of the SHS fluid. The functional form of c (3) has been estimated by different authors based on assumptions regarding its range [31,32] or its factorization in terms of c(r) [33]. In order to yield reasonable agreement with computer simulations all these extensions of the DFT by Choudhury and Ghosh [30] require an additional, density dependent, fitting parameter which is chosen such that the correct contact value of the density profile or the correct bulk pressure is guaranteed.…”

Section: Introductionmentioning

confidence: 99%

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A fundamental measure theory for the sticky hard sphere fluid

Hansen-Goos

Wettlaufer

2011

The Journal of Chemical Physics

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We construct a density functional theory (DFT) for the sticky hard sphere (SHS) fluid which, like Rosenfeld's fundamental measure theory (FMT) for the hard sphere fluid [Phys. Rev. Lett. 63, 980 (1989)], is based on a set of weighted densities and an exact result from scaled particle theory (SPT). It is demonstrated that the excess free energy density of the inhomogeneous SHS fluid ΦSHS is uniquely defined when (a) it is solely a function of the weighted densities from Kierlik and Rosinberg's version of FMT [Phys. Rev. A 42, 3382 (1990)], (b) it satisfies the SPT differential equation, and (c) it yields any given direct correlation function (DCF) from the class of generalized Percus-Yevick closures introduced by Gazzillo and Giacometti [J. Chem. Phys. 120, 4742 (2004)]. The resulting DFT is shown to be in very good agreement with simulation data. In particular, this FMT yields the correct contact value of the density profiles with no adjustable parameters. Rather than requiring higher order DCFs, such as perturbative DFTs, our SHS FMT produces them. Interestingly, although equivalent to Kierlik and Rosinberg's FMT in the case of hard spheres, the set of weighted densities used for Rosenfeld's original FMT is insufficient for constructing a DFT which yields the SHS DCF.

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“…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.…”

Section: Theorymentioning

confidence: 99%

Response behavior of diblock copolymer brushes in explicit solvent

Gong

Marshall

Chapman

2012

The Journal of Chemical Physics

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The understanding of phase behavior of copolymer brushes is of fundamental importance for the design of smart materials. In this paper, we have performed classical density functional theory calculations to study diblock copolymer brushes (A-B) in an explicit solvent which prefers the A block to B block. With increasing B-block length (N(B)), we find a structural transition of the copolymer brush from mixed to collapsed, partial-exposed, and exposed structure, which is qualitatively consistent with experiments. The phase transitions are attributed to the interplay between entropic cost of folding copolymer brushes and enthalpic effect of contact between unlike components. In addition, we examine the effect of different parameters, such as grafting density (ρ(g)), the bottom block length (N(A)), and the chain length of solvent (N(S)) on the solvent response of copolymer brushes. The transition chain length (N(B)) increases with decreasing ρ(g) and N(A), and a smaller solvent molecule makes the collapsed structure less stable due to its lower penetration cost. Our results provide the insight to phase behavior of copolymer brushes in selective solvents from a molecular view.

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Density functional approximations for confined classical fluids

Cited by 30 publications

References 30 publications

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

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

A fundamental measure theory for the sticky hard sphere fluid

Response behavior of diblock copolymer brushes in explicit solvent

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