A density functional theory for inhomogeneous charged fluids

Evans, Robert; Sluckin, T. J.

doi:10.1080/00268978000101581

Cited by 135 publications

(138 citation statements)

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“…7, f id b is the bulk ideal energy density defined by β −1 i c i (ln c i Λ 3 i − 1) and V is the system volume [10]. On the other hand, Ω b can also be determined from the thermodynamic relation…”

Section: Bulk Fluid Equation Of Statementioning

confidence: 99%

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A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson–Nernst–Planck Equations to Account for Hard Sphere Repulsion Among Ions

et al. 2016

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The hard sphere repulsion among ions can be considered in the Poisson-Nernst-Planck (PNP) equations by combining the fundamental measure theory (FMT). To reduce the nonlocal computational complexity in 3D simulation of biological systems, a local approximation of FMT is derived, which forms a local hard sphere PNP (LHSPNP) model. In the derivation, the excess chemical potential from hard sphere repulsion is obtained with the FMT and has six integration components. For the integrands and weighted densities in each component, Taylor expansions are performed and the lowest order approximations are taken, which result in the final local hard sphere (LHS) excess chemical potential with four components. By plugging the LHS excess chemical potential into the ionic flux expression in the Nernst-Planck equation, the three dimensional LHSPNP is obtained. It is interestingly found that the essential part of free energy term of the previous size modified model (Borukhov et al Phys. Rev. Lett. 1997, 79, 435-438; Kilic et al Phys. Rev. E 2007, 75, 021502; Lu and Zhou Biophys. J. 2011, 100, 2475-2485; Liu and Eisenberg J. Chem. Phys. 2014, 141, 22D532) has a very similar form to one term of the LHS model, but LHSPNP has more additional terms accounting for size effects. Equation of state for one component homogeneous fluid is studied for the local hard sphere approximation of FMT and is proved to be exact for the first two virial coefficients, while the previous size modified model only presents the first virial coefficient accurately. To investigate the effects of LHS model and the competitions among different counterion species, numerical experiments are performed for the traditional PNP model, the LHSPNP model, the previous size modified PNP (SMPNP) model and the Monte Carlo simulation. It's observed that in steady state the LHSPNP results are quite different from the PNP results, but are close to the SMPNP results under a wide range of boundary conditions. Besides, in both LHSPNP and SMPNP models the stratification of one counterion species can be observed under certain bulk concentrations.

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Section: Bulk Fluid Equation Of Statementioning

confidence: 99%

“…In uniform fluid with constant density, the equation of state for FMT is known to be the PercusYevick compressibility equation, which is the same as the scaled particle theory [10,45,54]. The four scalar weighted densities {n α }(α = 0, 1, 2, 3) can be reduced to {ξ (α) } where…”

Section: Bulk Fluid Equation Of Statementioning

confidence: 99%

A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson–Nernst–Planck Equations to Account for Hard Sphere Repulsion Among Ions

et al. 2016

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“…If correlations are neglected in this attractive term, the DFT reduces to a mean-field ͑van der Waals͒ treatment. 16 Compared to the effort devoted to the development of an accurate description of the reference term ͑e.g., with the use of WDAs͒, 13,15 less attention has been placed on the incorporation of correlations in the perturbative term since the early work of Toxvaerd. [17][18][19] An adequate treatment of the correlations in the attractive term is crucial for an accurate description of both the fluid phase equilibria and the interfacial properties.…”

Section: Introductionmentioning

confidence: 99%

“…The most popular and successful molecular description of interfacial systems invariably involves a DFT treatment. The DFT approach has been described in detail by a number of authors including Evans, 13 Davis,14 and Winkelmann,15 who have discussed the general formalism and the various approximations including perturbation expansions, the local density approximation ͑LDA͒, and the weighted density approximation ͑WDA͒. The latter is necessary when dealing with highly oscillatory density profiles, as found in fluids close to a solid surface or in a confined geometry.…”

Section: Introductionmentioning

confidence: 99%

“…Though the study of inhomogeneous fluids has a long history from the early mechanical treatment of Laplace and Young, 11 through the square gradient approach of van der Waals, 11,12 to the present day molecular density functional theories ͑DFTs͒, 13 a quantitative description of the interfacial properties of inhomogeneous fluids such as the interfacial thickness, adsorption, wetting, and the surface tension is relatively rare, particularly in the case of molecules with complex interactions. Interfacial systems are ubiquitous in living systems ͑cell membranes are interfaces which control molecular transport and biological function͒ and are of fundamental industrial importance in areas as diverse as detergency ͑surfactants and solubilization͒, food production ͑emulsions and colloids͒, cosmetics ͑structures phases͒, and optoelectronic devices ͑liquid crystals͒.…”

Section: Introductionmentioning

confidence: 99%

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An accurate density functional theory for the vapor-liquid interface of associating chain molecules based on the statistical associating fluid theory for potentials of variable range

Gloor

Jackson

Blas

et al. 2004

The Journal of Chemical Physics

119

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A Helmholtz free energy density functional is developed to describe the vapor-liquid interface of associating chain molecules. The functional is based on the statistical associating fluid theory with attractive potentials of variable range ͑SAFT-VR͒ for the homogenous fluid ͓A. Gil-Villegas, A. Galindo, P. J. Whitehead, S. J. Mills, G. Jackson, and A. N. Burgess, J. Chem. Phys. 106, 4168 ͑1997͔͒. A standard perturbative density functional theory ͑DFT͒ is constructed by partitioning the free energy density into a reference term ͑which incorporates all of the short-range interactions, and is treated locally͒ and an attractive perturbation ͑which incorporates the long-range dispersion interactions͒. In our previous work ͓F. J. Blas, E. Martín del Río, E. de Miguel, and G. Jackson, Mol. Phys. 99, 1851 ͑2001͒; G. J. Gloor, F. J. Blas, E. Martín del Río, E. de Miguel, and G. Jackson, Fluid Phase Equil. 194, 521 ͑2002͔͒ we used a mean-field version of the theory ͑SAFT-HS͒ in which the pair correlations were neglected in the attractive term. This provides only a qualitative description of the vapor-liquid interface, due to the inadequate mean-field treatment of the vapor-liquid equilibria. Two different approaches are used to include the correlations in the attractive term: in the first, the free energy of the homogeneous fluid is partitioned such that the effect of correlations are incorporated in the local reference term; in the second, a density averaged correlation function is incorporated into the perturbative term in a similar way to that proposed by Toxvaerd ͓S. Toxvaerd, J. Chem. Phys. 64, 2863 ͑1976͔͒. The latter is found to provide the most accurate description of the vapor-liquid surface tension on comparison with new simulation data for a square-well fluid of variable range. The SAFT-VR DFT is used to examine the effect of molecular chain length and association on the surface tension. Different association schemes ͑dimerization, straight and branched chain formation, and network structures͒ are examined separately. The surface tension of the associating fluid is found to be bounded between the nonassociating and fully associated limits ͑both of which correspond to equivalent nonassociating systems͒. The temperature dependence of the surface tension is found to depend strongly on the balance between the strength and range of the association, and on the particular association scheme. In the case of a system with a strong but very localized association interaction, the surface tension exhibits the characteristic ''s shaped'' behavior with temperature observed in fluids such as water and alkanols. The various types of curves observed in real substances can be reproduced by the theory. It is very gratifying that a DFT based on SAFT-VR free energy can provide an accurate quantitative description of the surface tension of both the model and experimental systems.

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Structure of the Electric Double Layer

Blum¹

1990

Advances in Chemical Physics

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A density functional theory for inhomogeneous charged fluids

Cited by 135 publications

References 28 publications

A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson–Nernst–Planck Equations to Account for Hard Sphere Repulsion Among Ions

A Local Approximation of Fundamental Measure Theory Incorporated into Three Dimensional Poisson–Nernst–Planck Equations to Account for Hard Sphere Repulsion Among Ions

An accurate density functional theory for the vapor-liquid interface of associating chain molecules based on the statistical associating fluid theory for potentials of variable range

Structure of the Electric Double Layer

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