Proper integral equations for interaction-site fluids: Exact free-energy expressions

L. Lue, D. Blankschtein

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We have developed expressions for the residual Helmholtz free energy and the residual chemical potential in terms of the correlation functions and bridge functions in the context of the interaction-site formalism for the Chandler-Silbey-Ladanyi equations. Unlike the corresponding expressions for the extended-RISM equation, these expressions are formally exact for systems described by interaction-site models. The new expressions are similar in form to those for multicomponent simple fluid mixtures and are found to reduce to them in the extended-atom limit, where the bond lengths approach infinity. We have also found that the residual Helmholtz free energy satisfies a variational principle for a certain class of closure relations. This finding could facilitate the development of more efficient methods for solving the Chandler- Silbey-Ladanyi equations. We have also derived explicit expressions for the residual Helmholtz free energy, residual chemical potential, residual pressure, and residual internal energy in the hypernetted-chain approximation of the Chandler- Silbey-Ladanyi equations. It is noteworthy that the derived expressions depend solely on the correlation functions of the system at full coupling, thus making the computation of the various fluid properties simpler and more efficient by eliminating the need to perform a numerical integration over a coupling constant. We have also found that the residual Helmholtz free energy associated with the hypernetted-chain approximation of the Chandler-Silbey-Ladanyi equations satisfies a variational principle. Furthermore, in the extended-atom limit, all the derived expressions associated with the hypernetted-chain approximation of the Chandler- Silbey-Ladanyi equations reduce to those corresponding to the multicomponent simple fluid mixtures.
LanguageEnglish
Pages3002-3012
Number of pages11
JournalJournal of Chemical Physics
Volume100
Issue number4
DOIs
Publication statusPublished - 15 Feb 1994

Fingerprint

Free energy
Integral equations
integral equations
free energy
Fluids
fluids
Chemical potential
interactions
Atoms
variational principles
Bond length
approximation
internal energy
numerical integration
infinity
closures
atoms
formalism

Keywords

  • rism approximation
  • molecular fluids
  • dielectric-constant
  • potential functions
  • phase-diagrams
  • liquids
  • water
  • thermodynamics
  • formalism
  • diatomics

Cite this

@article{0b0ba338ff94481f9663ad3674065972,
title = "Proper integral equations for interaction-site fluids: Exact free-energy expressions",
abstract = "We have developed expressions for the residual Helmholtz free energy and the residual chemical potential in terms of the correlation functions and bridge functions in the context of the interaction-site formalism for the Chandler-Silbey-Ladanyi equations. Unlike the corresponding expressions for the extended-RISM equation, these expressions are formally exact for systems described by interaction-site models. The new expressions are similar in form to those for multicomponent simple fluid mixtures and are found to reduce to them in the extended-atom limit, where the bond lengths approach infinity. We have also found that the residual Helmholtz free energy satisfies a variational principle for a certain class of closure relations. This finding could facilitate the development of more efficient methods for solving the Chandler- Silbey-Ladanyi equations. We have also derived explicit expressions for the residual Helmholtz free energy, residual chemical potential, residual pressure, and residual internal energy in the hypernetted-chain approximation of the Chandler- Silbey-Ladanyi equations. It is noteworthy that the derived expressions depend solely on the correlation functions of the system at full coupling, thus making the computation of the various fluid properties simpler and more efficient by eliminating the need to perform a numerical integration over a coupling constant. We have also found that the residual Helmholtz free energy associated with the hypernetted-chain approximation of the Chandler-Silbey-Ladanyi equations satisfies a variational principle. Furthermore, in the extended-atom limit, all the derived expressions associated with the hypernetted-chain approximation of the Chandler- Silbey-Ladanyi equations reduce to those corresponding to the multicomponent simple fluid mixtures.",
keywords = "rism approximation, molecular fluids, dielectric-constant, potential functions, phase-diagrams, liquids, water, thermodynamics, formalism, diatomics",
author = "L. Lue and D. Blankschtein",
note = "English Article MX628 J CHEM PHYS",
year = "1994",
month = "2",
day = "15",
doi = "10.1063/1.466441",
language = "English",
volume = "100",
pages = "3002--3012",
journal = "Journal of Chemical Physics",
issn = "0021-9606",
number = "4",

}

Proper integral equations for interaction-site fluids: Exact free-energy expressions. / Lue, L.; Blankschtein, D.

In: Journal of Chemical Physics, Vol. 100, No. 4, 15.02.1994, p. 3002-3012.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Proper integral equations for interaction-site fluids: Exact free-energy expressions

AU - Lue, L.

AU - Blankschtein, D.

N1 - English Article MX628 J CHEM PHYS

PY - 1994/2/15

Y1 - 1994/2/15

N2 - We have developed expressions for the residual Helmholtz free energy and the residual chemical potential in terms of the correlation functions and bridge functions in the context of the interaction-site formalism for the Chandler-Silbey-Ladanyi equations. Unlike the corresponding expressions for the extended-RISM equation, these expressions are formally exact for systems described by interaction-site models. The new expressions are similar in form to those for multicomponent simple fluid mixtures and are found to reduce to them in the extended-atom limit, where the bond lengths approach infinity. We have also found that the residual Helmholtz free energy satisfies a variational principle for a certain class of closure relations. This finding could facilitate the development of more efficient methods for solving the Chandler- Silbey-Ladanyi equations. We have also derived explicit expressions for the residual Helmholtz free energy, residual chemical potential, residual pressure, and residual internal energy in the hypernetted-chain approximation of the Chandler- Silbey-Ladanyi equations. It is noteworthy that the derived expressions depend solely on the correlation functions of the system at full coupling, thus making the computation of the various fluid properties simpler and more efficient by eliminating the need to perform a numerical integration over a coupling constant. We have also found that the residual Helmholtz free energy associated with the hypernetted-chain approximation of the Chandler-Silbey-Ladanyi equations satisfies a variational principle. Furthermore, in the extended-atom limit, all the derived expressions associated with the hypernetted-chain approximation of the Chandler- Silbey-Ladanyi equations reduce to those corresponding to the multicomponent simple fluid mixtures.

AB - We have developed expressions for the residual Helmholtz free energy and the residual chemical potential in terms of the correlation functions and bridge functions in the context of the interaction-site formalism for the Chandler-Silbey-Ladanyi equations. Unlike the corresponding expressions for the extended-RISM equation, these expressions are formally exact for systems described by interaction-site models. The new expressions are similar in form to those for multicomponent simple fluid mixtures and are found to reduce to them in the extended-atom limit, where the bond lengths approach infinity. We have also found that the residual Helmholtz free energy satisfies a variational principle for a certain class of closure relations. This finding could facilitate the development of more efficient methods for solving the Chandler- Silbey-Ladanyi equations. We have also derived explicit expressions for the residual Helmholtz free energy, residual chemical potential, residual pressure, and residual internal energy in the hypernetted-chain approximation of the Chandler- Silbey-Ladanyi equations. It is noteworthy that the derived expressions depend solely on the correlation functions of the system at full coupling, thus making the computation of the various fluid properties simpler and more efficient by eliminating the need to perform a numerical integration over a coupling constant. We have also found that the residual Helmholtz free energy associated with the hypernetted-chain approximation of the Chandler-Silbey-Ladanyi equations satisfies a variational principle. Furthermore, in the extended-atom limit, all the derived expressions associated with the hypernetted-chain approximation of the Chandler- Silbey-Ladanyi equations reduce to those corresponding to the multicomponent simple fluid mixtures.

KW - rism approximation

KW - molecular fluids

KW - dielectric-constant

KW - potential functions

KW - phase-diagrams

KW - liquids

KW - water

KW - thermodynamics

KW - formalism

KW - diatomics

UR - http://jcp.aip.org/resource/1/jcpsa6/v100/i4/p3002_s1?isAuthorized=no

U2 - 10.1063/1.466441

DO - 10.1063/1.466441

M3 - Article

VL - 100

SP - 3002

EP - 3012

JO - Journal of Chemical Physics

T2 - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 4

ER -