Density functional theory for Yukawa fluids

Hatlo, Marius M.; Banerjee, Priyanka; Forsman, Jan; Lue, Leo

doi:10.1063/1.4742154

Cited by 5 publications

(5 citation statements)

References 21 publications

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“…Similar results are found with the theory for point charge counterions. 46 The results of the splitting theory can be improved by including the next order cumulant correction to the short-wavelength fluctuations of the electrostatic potential; 46 this is equivalent of incorporating the second order virial term in the short-ranged electrostatic interactions.…”

Section: Resultsmentioning

confidence: 99%

Recycling of Uranyl from Contaminated Water

et al. 2013

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Many separation processes are related to the behavior of ions close to charged surfaces. In this work, we examine uranyl ions, which can be considered as rod-like molecular ions with a spatially distributed charge, embedded in a system of like charged surfaces. The analysis of the system is based on an approximate field theory which is accurate from the weak to the strong electrostatic coupling regimes. The numerical results show that close to the charged surface the ions are oriented parallel to the surface, whereas at distances greater than half of the ion length, they are randomly oriented. Due to the restriction of the orientational degrees of freedom, the density of ions at the charged surface decreases to zero. For large surface charge densities, the force between like charged surfaces becomes attractive, as a result of charge correlations. The theoretical results are in good agreement with Monte Carlo simulation results.

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Section: Resultsmentioning

confidence: 99%

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“…The long-wavelength contributions are treated using a mean-field approximation. With these approximations, the free energy functional F of the system is given by 18,19,24 βF…”

Section: B Splitting Theorymentioning

confidence: 99%

“…However, the dependence of the parameter σ within the splitting theory allows it to give the correct prediction of the power law, but changing the level of approximation of the integration of the short-range fluctuations will change the precise value of the proportionality constant. Consequently, it is able to give 24 an excellent description of the pressure in the two plate geometry from the strong-to weak-coupling limits.…”

Section: B Splitting Theorymentioning

confidence: 99%

Ions confined in spherical dielectric cavities modeled by a splitting field-theory

Lue

Linse

2015

The Journal of Chemical Physics

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The properties of ions confined within spherical dielectric cavities are examined by a splitting field-theory and Monte Carlo simulations. Three types of cavities are considered: one possessing a uniform surface charge density, one with a uniform volume charge density, and one containing mobile ions. In all cases, mobile counterions are present within the dielectric sphere. The splitting theory is based on dividing the electrostatic interaction into long- and short-wavelength contributions and applying different approximations on the two contributions. The splitting theory works well for the case where the dielectric constant of the confining sphere is equal to or less than that of the medium external to the sphere. Nevertheless, by extending the theory with a virial expansion, the predictions are improved. However, when the dielectric constant of the confining sphere is greater than that of the medium outside the sphere, the splitting theory performs poorly, only qualitatively agreeing with the simulation data. In this case, the strong-coupling expansion does not seem to work well, and a modified mean-field theory where the counterions interact directly with only their own image charge gives improved predictions. The splitting theory works best for the system with a uniform surface charge density and worst for the system with a uniform volume charge density. Increasing the number of ions within the sphere, at a fixed radius, tends to increase the ion density near the surface of the sphere and leads to a depletion region in the sphere interior; however, varying the ion number does not lead to any qualitative changes in the performance of the splitting theory.

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“…This is essentially the form of the free energy given by the splitting theory at the second order cumulant expansion of the short wavelength fluctuating field. This theory has been successfully used to model the properties of systems interacting with the Yukawa potential 34 . The main exception is the presence of the next to final term in Eq.…”

Section: Splitting Theorymentioning

confidence: 99%

A diagrammatic analysis of the variational perturbation method for classical fluids

Lue

2018

Soft Matter

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The statistical mechanics of classical fluids can be approached from the particle perspective, where the focus is on the various positions and interactions of the particles, and from the field perspective, where the focus is on the form of the interaction fields generated by the particles. In this work, we combine these two perspectives by examining the variational perturbation method for classical fluids, which has been widely used to describe nonuniform electrolyte systems. Most of this work has been for low orders of the approximation, it has been limited to cases where the electrostatic interactions are weak. We present an exact diagrammatic representation of the method, which greatly facilitates the enumeration and evaluation of higher order corrections to the free energy functional. This framework is able to encapsulate several different approximate theories. Performing a cumulant expansion, leads to the Debye-Hückel and higher order corrections. Including the contribution of chain diagrams leads to a theory closely related to the splitting theory [Hatlo and Lue, Europhys. Lett., 2010, 89, 25002], which has been shown to be accurate from the weak through to the strong coupling limits. Including all chain and ring diagrams leads to the hypernetted chain approximation; this is a more direct route to the conventional derivation, which also requires a renormalization of the Mayer f-bonds to the total correlation functions. These approximations to the variational perturbation method are applied to the classical one-component plasma in order to assess their relative accuracy and understand their relationship to each other. Strategies for developing improved approximations are discussed.

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Density functional theory for Yukawa fluids

Cited by 5 publications

References 21 publications

Recycling of Uranyl from Contaminated Water

Recycling of Uranyl from Contaminated Water

Ions confined in spherical dielectric cavities modeled by a splitting field-theory

A diagrammatic analysis of the variational perturbation method for classical fluids

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