A variational approach to the theory of ionic solutions

Olivares, Wilmer; McQuarrie, Donald A.

doi:10.1063/1.433545

Cited by 35 publications

(17 citation statements)

References 26 publications

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“…Taking the problem from the other side, one can first search for the functionals of h(r) that yields the OZ equation with a chosen closure relation, here: the HNC closure. Such a systematic approach is exposed in [4]. Once these are found, one can then pick among them a functional that fulfills the charging relation.…”

Section: Key Steps Of Lado's Calculationmentioning

confidence: 99%

“…In Ref. [4], the mean spherical model, which is closely related to the DH model, is addressed in order to find a generating functional of the direct correlation function. However, one can use the results of [4] in order to obtain the functional of Eq.…”

Section: Alternative Debye-hückel Free-energy Functionalmentioning

confidence: 99%

“…In the present addendum, we update our results by providing simpler functionals that have the same properties. We relate these functionals to the approaches of Lado [3] and of Olivares and McQuarrie [4]. We also discuss briefly the non-uniqueness issue that is raised by these results.…”

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confidence: 91%

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Free-energy functional of the Debye-Hückel model of simple fluids

Piron

Błeński

2016

Phys. Rev. E

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The Debye-Hückel approximation to the free energy of a simple fluid is written as a functional of the pair correlation function. This functional can be seen as the Debye-Hückel equivalent to the functional derived in the hypernetted chain framework by Morita and Hiroike, as well as by Lado. It allows one to obtain the Debye-Hückel integral equation through a minimization with respect to the pair correlation function, leads to the correct form of the internal energy, and fulfills the virial theorem.

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Section: Key Steps Of Lado's Calculationmentioning

confidence: 99%

Section: Alternative Debye-hückel Free-energy Functionalmentioning

confidence: 99%

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Free-energy functional of the Debye-Hückel model of simple fluids

Piron

Błeński

2016

Phys. Rev. E

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“…We found useful to recast the ORPA equations in the framework of the generating functionals for the integral equations of the theory of liquids [17]. We show that the two different first-order expansions of the free energy functional corresponding to the well known Gibbs-Bogolioubov and Weeks-Chandler and Andersen approximations for the free energy [18] can be transformed into two closely related forms of the ORPA by addition of the same functional.…”

Section: Introductionmentioning

confidence: 97%

Optimized random-phase approximations for arbitrary reference systems: Extremum conditions and thermodynamic consistence

et al. 1998

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The optimized random phase approximation (ORPA) for classical liquids is re-examined in the framework of the generating functional approach to the integral equations. We show that the two main variants of the approximation correspond to the addition of the same correction to two different first order approximations of the homogeneous liquid free energy. Furthermore, we show that it is possible to consistently use the ORPA with arbitrary reference systems described by continuous potentials and that the same approximation is equivalent to a particular extremum condition for the corresponding generating functional. Finally, it is possible to enforce the thermodynamic consistence between the thermal and the virial route to the equation of state by requiring the global extremum condition on the generating functional.61.20 -p, 61.20.Gy

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“…then the functional can be written18 where F 0 is a constant. In this case, B[h i (x)] is found by rearranging eq 1:Written in this manner, B[h i (x)] ) δF[h(x)]/δh(x) ) 0,and eq 5 can be used to obtain the functional F[h(x)].…”

mentioning

confidence: 99%

Ion Adsorption in the Electrical Double Layer: Variational Solution to the Hypernetted Chain Equations

Greathouse

McQuarrie

1996

J. Phys. Chem.

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In order to investigate the effect of specific adsorption of counterions onto a charged planar surface, the HNC/MSA equations were solved using a variational method. Ion adsorption is introduced through a sticky potential. The variational method involves a simple computational algorithm, and although it does not yield exact solutions, the contact condition and electroneutrality are automatically satisfied. Results are presented for a surface charge density of -0.10 C m -2 and for a range of bulk ion concentrations of 1:1 electrolyte and counterion adsorption tendencies. While the sticky potential provides a simple model of wall-ion interactions, the effect of increasing ion adsorption on the structure of the double layers can be seen. Comparisons are also made with the modified Gouy-Chapman theory, which neglects the finite size of the ions. At high bulk ion concentrations, ion size effects result in nonmonotonic ion distributions.

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A variational approach to the theory of ionic solutions

Cited by 35 publications

References 26 publications

Free-energy functional of the Debye-Hückel model of simple fluids

Free-energy functional of the Debye-Hückel model of simple fluids

Optimized random-phase approximations for arbitrary reference systems: Extremum conditions and thermodynamic consistence

Ion Adsorption in the Electrical Double Layer: Variational Solution to the Hypernetted Chain Equations

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