Integral equation approximations for inhomogeneous fluids: functional optimization

Bush, Michael R.; Booth, Michael J.; Haymet, A. D. J.; Schlijper, A. G.

doi:10.1080/00268979809483194

Cited by 9 publications

(8 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As our results apply to the full entropy functional, they are valuable to any functional minimization as, e.g., those in [4,5]. It can also be mentioned that this theorem does not conflict with Laird-Haymet [11].…”

Section: Series Summationsupporting

confidence: 51%

“…The problem is not the lack of exact expressions but to derive equations that are both accurate and manageable from a theoretical and numerical point of view. Amongst the exact expressions we cite the classical work of Nettleton and Green [1], and, more recently, [2,3], while approximate expressions can be found in [3][4][5][6][7]. In [4] we have shown how an infinite subset of terms (dependent exclusively on the one-and two-body distribution functions) can be analytically summed giving rise to the so-called ring approximation and, through a minimization of the free energy functional, the well known HNC approximation [8] is obtained as an optimized superposition approximation.…”

Section: Introductionmentioning

confidence: 99%

“…In [4] we have shown how an infinite subset of terms (dependent exclusively on the one-and two-body distribution functions) can be analytically summed giving rise to the so-called ring approximation and, through a minimization of the free energy functional, the well known HNC approximation [8] is obtained as an optimized superposition approximation. Later on, Bush et al [5] derived sets of integral equations by analyzing several levels of approximation to the grand potential function and, in a recent and very interesting article, Puoskari [3] extends the ring approximation to three particle functions showing how the HNC2 equations either of the Wertheim [9] or the Baxter [10] variety can be obtained. Baranyai and Evans [6] showed that, even though the derivations are done in the grand canonical ensemble, the entropy equations are, in fact, ensemble invariants if local expressions are used for the entropy.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Density fluctuations and entropy

Hernando

Blum

2000

Phys. Rev. E

View full text Add to dashboard Cite

A functional for the entropy that is asymptotically correct both in the high- and low-density limits is proposed. The new form is S=S((id))+S((ln))+S((r))+S((c)), where the term S((c)) depends on the p-body density fluctuations alpha(p) and has the form S((c))/k=ln 2-1+ summation operator(infinity)(p=2) (ln 2)(p)/p! alpha(p)-[exp(alpha(2)-1)-alpha(2)]+Sinsertion mark. Sinsertion mark renormalizes the ring approximation S((r)). This result is obtained by analyzing the functional dependence of the most general expression of the entropy. Two main results for S((c)) are proved: (i) In the thermodynamic limit it is only a functional of the one-body distribution function and (ii) by summing to infinite order the leading contributions in the density a numerical expression for the entropy [Eq. (33)] with a renormalized ring approximation is obtained. The relation of these results to the incompressible approximation for the entropy is discussed and preliminary numerical results on hard spheres are presented.

show abstract

Section: Series Summationsupporting

confidence: 51%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Density fluctuations and entropy

Hernando

Blum

2000

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…The ∆S uv HN C can be split into the ideal gas entropy change, given by ∆S id HN C = −k ρ|ln g + k ∆ρ|1 , as well the excess (or ring entropy, as it has been referred to by some authors 144,145 ) contribution ∆S ex HN C = k/2 ∆ρ|C|∆ρ . The minimization of the grand potential leads to…”

Section: Effect Of Corrections On Solvation Thermodynamicsmentioning

confidence: 99%

Can approximate integral equation theories accurately predict solvation thermodynamics?

Misin

2017

Preprint

View full text Add to dashboard Cite

Department of Physics Doctor of PhilosophyCan approximate integral equation theories accurately predict solvation thermodynamics? by Maksim MisinThe thesis focuses on the prediction of solvation thermodynamics using integral equation theories. Our main goal is to improve the approach using a rational correction. We achieve it by extending recently introduced pressure correction, and rationalizing it in the context of solvation entropy. The improved model (to which we refer as advanced pressure correction) is rather universal. It can accurately predict solvation free energies in water at both ambient and non-ambient temperatures, is capable of addressing ionic solutes and salt solutions, and can be extended to non-aqueous systems. The developed approach can be used to model processes in biological systems, as well as to extend related theoretical models further.First of all, I would like to thank my supervisors, Prof. Maxim V. Fedorov and Dr. David S. Palmer, who made this Ph.D. an amazing experience. They offered me guidance and support, helping me not only to start but also to finish this project. I would like to acknowledge two visiting students Petteri A. Vainikka, and Samuel W. Coles, who turned out to be wonderful collaborators. Various Strathclyde postgraduate students: Ivor

show abstract

“…More recently, the pair approximation has been further applied in wider contexts by Kjellander and coworkers.24h28 Work on the charged surface/electrolyte interface has largely used the charged hard-sphere/charged hard-wall potential model, rather than the more realistic " soft Ï potentials used here and in our previous work.13,29 A compact derivation of both pair and singlet approximations has also been presented by our group. 30 This paper is organized as follows. The equations and numerical details used in this work are presented in Section II.…”

Section: The Electrical Double Layermentioning

confidence: 99%

Electrolytes at charged interfaces: Ion–ion–interface three-body correlation functions

Eaton

Goodyear

Haymet

2001

Phys. Chem. Chem. Phys.

Self Cite

View full text Add to dashboard Cite

Inhomogeneous correlation functions for model " soft Ï 2È2 and 1È1 electrolytes at a charged interface have been determined by the soÈcalled " pair Ï approximation of integral equation theory. The solvent is modeled as a structureless dielectric continuum at 25 ¡C. The wallÈionÈion structure is calculated using the inhomogeneous OrnsteinÈZernike relation, together with the hypernetted chain closure, and one of two choices for the functional relationship between the singlet and pair correlation functions. Both the interfacial density proÐles and the inhomogeneous pair correlation functions are calculated. For most cases, the inhomogeneous pair correlation functions near the interface vary signiÐcantly from the homogeneous pair correlation functions. This deviation generally becomes stronger as the charge on the surface increases, and the deviation generally extends out further from the interface as the surface charge increases. The density proÐles predicted by the pair approximations generally show less structure than the singlet approximation density proÐles, whereas the inhomogeneous pair correlation functions generally predict more structure than would be expected by simply assuming bulk pair correlation functions. The density proÐles and inhomogeneous correlation functions are also found to agree qualitatively with previous simulations which used " charged hardÈsphere/charged hardÈwall Ï potentials.

show abstract

Integral equation approximations for inhomogeneous fluids: functional optimization

Cited by 9 publications

References 31 publications

Density fluctuations and entropy

Density fluctuations and entropy

Can approximate integral equation theories accurately predict solvation thermodynamics?

Electrolytes at charged interfaces: Ion–ion–interface three-body correlation functions

Contact Info

Product

Resources

About