Fundamental measure theory for hard-sphere mixtures revisited: the White Bear version

Roth, Roland; Evans, Robert; Lang, Andreas; Kahl, Gerhard

doi:10.1088/0953-8984/14/46/313

Cited by 626 publications

(832 citation statements)

References 34 publications

Supporting

Mentioning

812

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

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

View full text Add to dashboard Cite

show abstract

“…In analogy to Φ RF the substitutions n 1 n 2 → n 1 n 2 − n 1 · n 2 and n 3 2 → n 3 2 − 3n 2 n 2 · n 2 are made in Φ. The resulting functional Φ WB is called the White-Bear version of FMT [11]. In virtue of these substitutions, Φ WB has the correct low-density limit Eq.…”

Section: The New Functionalmentioning

confidence: 99%

“…Note, that consistency for the general hard-sphere mixture within the framework of FMT would always result in the less accurate pressure p PY . By following the recipe for the derivation of the original White-Bear version [11,12], described above, we calculate a new functional based on the pressure p CSIII For comparison we mention that in the above notation the original White-Bear functional Φ WB is recovered with φ WB 2 (n 3 ) ≡ 0 and…”

Section: The New Functionalmentioning

confidence: 99%

Density functional theory for hard-sphere mixtures: the White Bear version mark II

Hansen-Goos¹,

Roth²

2006

J. Phys.: Condens. Matter

193

286

View full text Add to dashboard Cite

Abstract. In the spirit of the White-Bear version of fundamental measure theory we derive a new density functional for hard-sphere mixtures which is based on a recent mixture extension of the Carnahan-Starling equation of state. In addition to the capability to predict inhomogeneous density distributions very accurately, like the original White-Bear version, the new functional improves upon consistency with an exact scaled-particle theory relation in the case of the pure fluid. We examine consistency in detail within the context of morphological thermodynamics. Interestingly, for the pure fluid the degree of consistency of the new version is not only higher than for the original White-Bear version but also higher than for Rosenfeld's original fundamental measure theory.

show abstract

“…Next is a hard-sphere contribution, F hs [ρ], for which the "White Bear" Fundamental Measure Theory (FMT) model was used [23,24] along with the Barker-Hendersen hard-sphere diameter [12,25]. The third contribution, the "core correction" F core [ρ], is similar to a FMT model but is constructed so that the total free energy functional reproduces a given equation of state in the bulk phase as well as certain other conditions concerning the direct correlation function in the bulk fluid [22].…”

Section: Theory a Density Functional Theorymentioning

confidence: 99%

Density functional theory of inhomogeneous liquids. III. Liquid-vapor nucleation

Lutsko

2008

The Journal of Chemical Physics

View full text Add to dashboard Cite

The process of nucleation of vapor bubbles from a superheated liquid and of liquid droplets from a supersaturated vapor is investigated using the Modified-Core van der Waals model Density Functional Theory (Lutsko, JCP 128, 184711 (2008)). A novel approach is developed whereby nucleation is viewed as a transition from a metastable state to a stable state via the minimum free energy path which is identified using the nudged elastic-band method for exploring free energy surfaces. This allows for the unbiased calculation of the properties of sub-and super-critical clusters, as well as of the critical cluster. For Lennard-Jones fluids, the results compare well to simulation and support the view that even at high supersaturation nucleation proceeds smoothly rather than via spinodal-like instabilities as has been suggested recently.

show abstract

Fundamental measure theory for hard-sphere mixtures revisited: the White Bear version

Cited by 626 publications

References 34 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

Density functional theory for hard-sphere mixtures: the White Bear version mark II

Density functional theory of inhomogeneous liquids. III. Liquid-vapor nucleation

Contact Info

Product

Resources

About