Integral equations for interaction site fluids --- The influence of connectivity constraints and auxiliary sites

L. Lue, D. Blankschtein

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We examine two central features of two well-known integral equations for interaction site fluids: ~i! the Chandler?Silbey?Ladanyi equations, and ~ii! the site?site Ornstein?Zernike equation. The first feature involves the influence of connectivity constraints. Specifically, we identify the restrictions imposed on the site?site correlation functions arising from the constraints of connectivity between sites within a molecule. We find that when the Chandler?Silbey?Ladanyi ~CSL! equations, a set of diagrammatically proper integral equations, are combined with a general approximate closure, they do not necessarily satisfy these connectivity constraints. On the other hand, the site?site Ornstein? Zernike ~SSOZ! equation, combined with a simple fluid closure, does satisfy these constraints. These findings profoundly affect the long-range behavior of the correlation functions and the dielectric constant of the bulk fluid. These findings are also important for the development of computational methods to obtain accurate numerical solutions of the CSL and SSOZ equations. When theories do not satisfy the above-mentioned connectivity constraints, we find that the resulting correlation functions do not satisfy the local neutrality constraints, which is a necessary requirement for any theory to properly predict the fluid dielectric constant. Instead, the correlation functions satisfy the constraints applicable to ionic fluids, that is, the Stillinger?Lovett moment conditions. This leads to the prediction of an infinite fluid dielectric constant. The second feature which we examine involves the influence of auxiliary sites on the prediction of the site?site total correlation functions.We prove that the addition of certain types of auxiliary sites does not affect the correlations between real sites when the Chandler?Silbey?Ladanyi equations are combined with a general approximate closure. The predictions of the SSOZ equation, combined with a general approximate closure, have been shown to depend on the presence of auxiliary sites. However, in the case of the Percus?Yevick closure for systems characterized by hard-sphere interaction sites, we are able to prove that the SSOZ equation does not exhibit this dependence for certain types of auxiliary sites.
LanguageEnglish
Pages5460-5470
Number of pages11
JournalJournal of Chemical Physics
Volume102
Issue number13
DOIs
Publication statusPublished - 1 Apr 1995

Fingerprint

Integral equations
integral equations
Fluids
closures
fluids
Permittivity
interactions
permittivity
predictions
Computational methods
constrictions
Molecules
moments
requirements
molecules

Keywords

  • molecular fluids
  • dielectric-constant
  • rism approximation
  • dipolar diatomics
  • phase-diagrams
  • thermodynamics
  • solvation
  • formalism
  • liquids

Cite this

@article{c8eb4aab09e24a3ba638dd6cbe939bb9,
title = "Integral equations for interaction site fluids --- The influence of connectivity constraints and auxiliary sites",
abstract = "We examine two central features of two well-known integral equations for interaction site fluids: ~i! the Chandler?Silbey?Ladanyi equations, and ~ii! the site?site Ornstein?Zernike equation. The first feature involves the influence of connectivity constraints. Specifically, we identify the restrictions imposed on the site?site correlation functions arising from the constraints of connectivity between sites within a molecule. We find that when the Chandler?Silbey?Ladanyi ~CSL! equations, a set of diagrammatically proper integral equations, are combined with a general approximate closure, they do not necessarily satisfy these connectivity constraints. On the other hand, the site?site Ornstein? Zernike ~SSOZ! equation, combined with a simple fluid closure, does satisfy these constraints. These findings profoundly affect the long-range behavior of the correlation functions and the dielectric constant of the bulk fluid. These findings are also important for the development of computational methods to obtain accurate numerical solutions of the CSL and SSOZ equations. When theories do not satisfy the above-mentioned connectivity constraints, we find that the resulting correlation functions do not satisfy the local neutrality constraints, which is a necessary requirement for any theory to properly predict the fluid dielectric constant. Instead, the correlation functions satisfy the constraints applicable to ionic fluids, that is, the Stillinger?Lovett moment conditions. This leads to the prediction of an infinite fluid dielectric constant. The second feature which we examine involves the influence of auxiliary sites on the prediction of the site?site total correlation functions.We prove that the addition of certain types of auxiliary sites does not affect the correlations between real sites when the Chandler?Silbey?Ladanyi equations are combined with a general approximate closure. The predictions of the SSOZ equation, combined with a general approximate closure, have been shown to depend on the presence of auxiliary sites. However, in the case of the Percus?Yevick closure for systems characterized by hard-sphere interaction sites, we are able to prove that the SSOZ equation does not exhibit this dependence for certain types of auxiliary sites.",
keywords = "molecular fluids, dielectric-constant, rism approximation, dipolar diatomics, phase-diagrams, thermodynamics, solvation, formalism, liquids",
author = "L. Lue and D. Blankschtein",
note = "English Article QP515 J CHEM PHYS",
year = "1995",
month = "4",
day = "1",
doi = "10.1063/1.469274",
language = "English",
volume = "102",
pages = "5460--5470",
journal = "Journal of Chemical Physics",
issn = "0021-9606",
number = "13",

}

Integral equations for interaction site fluids --- The influence of connectivity constraints and auxiliary sites. / Lue, L.; Blankschtein, D.

In: Journal of Chemical Physics, Vol. 102, No. 13, 01.04.1995, p. 5460-5470.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Integral equations for interaction site fluids --- The influence of connectivity constraints and auxiliary sites

AU - Lue, L.

AU - Blankschtein, D.

N1 - English Article QP515 J CHEM PHYS

PY - 1995/4/1

Y1 - 1995/4/1

N2 - We examine two central features of two well-known integral equations for interaction site fluids: ~i! the Chandler?Silbey?Ladanyi equations, and ~ii! the site?site Ornstein?Zernike equation. The first feature involves the influence of connectivity constraints. Specifically, we identify the restrictions imposed on the site?site correlation functions arising from the constraints of connectivity between sites within a molecule. We find that when the Chandler?Silbey?Ladanyi ~CSL! equations, a set of diagrammatically proper integral equations, are combined with a general approximate closure, they do not necessarily satisfy these connectivity constraints. On the other hand, the site?site Ornstein? Zernike ~SSOZ! equation, combined with a simple fluid closure, does satisfy these constraints. These findings profoundly affect the long-range behavior of the correlation functions and the dielectric constant of the bulk fluid. These findings are also important for the development of computational methods to obtain accurate numerical solutions of the CSL and SSOZ equations. When theories do not satisfy the above-mentioned connectivity constraints, we find that the resulting correlation functions do not satisfy the local neutrality constraints, which is a necessary requirement for any theory to properly predict the fluid dielectric constant. Instead, the correlation functions satisfy the constraints applicable to ionic fluids, that is, the Stillinger?Lovett moment conditions. This leads to the prediction of an infinite fluid dielectric constant. The second feature which we examine involves the influence of auxiliary sites on the prediction of the site?site total correlation functions.We prove that the addition of certain types of auxiliary sites does not affect the correlations between real sites when the Chandler?Silbey?Ladanyi equations are combined with a general approximate closure. The predictions of the SSOZ equation, combined with a general approximate closure, have been shown to depend on the presence of auxiliary sites. However, in the case of the Percus?Yevick closure for systems characterized by hard-sphere interaction sites, we are able to prove that the SSOZ equation does not exhibit this dependence for certain types of auxiliary sites.

AB - We examine two central features of two well-known integral equations for interaction site fluids: ~i! the Chandler?Silbey?Ladanyi equations, and ~ii! the site?site Ornstein?Zernike equation. The first feature involves the influence of connectivity constraints. Specifically, we identify the restrictions imposed on the site?site correlation functions arising from the constraints of connectivity between sites within a molecule. We find that when the Chandler?Silbey?Ladanyi ~CSL! equations, a set of diagrammatically proper integral equations, are combined with a general approximate closure, they do not necessarily satisfy these connectivity constraints. On the other hand, the site?site Ornstein? Zernike ~SSOZ! equation, combined with a simple fluid closure, does satisfy these constraints. These findings profoundly affect the long-range behavior of the correlation functions and the dielectric constant of the bulk fluid. These findings are also important for the development of computational methods to obtain accurate numerical solutions of the CSL and SSOZ equations. When theories do not satisfy the above-mentioned connectivity constraints, we find that the resulting correlation functions do not satisfy the local neutrality constraints, which is a necessary requirement for any theory to properly predict the fluid dielectric constant. Instead, the correlation functions satisfy the constraints applicable to ionic fluids, that is, the Stillinger?Lovett moment conditions. This leads to the prediction of an infinite fluid dielectric constant. The second feature which we examine involves the influence of auxiliary sites on the prediction of the site?site total correlation functions.We prove that the addition of certain types of auxiliary sites does not affect the correlations between real sites when the Chandler?Silbey?Ladanyi equations are combined with a general approximate closure. The predictions of the SSOZ equation, combined with a general approximate closure, have been shown to depend on the presence of auxiliary sites. However, in the case of the Percus?Yevick closure for systems characterized by hard-sphere interaction sites, we are able to prove that the SSOZ equation does not exhibit this dependence for certain types of auxiliary sites.

KW - molecular fluids

KW - dielectric-constant

KW - rism approximation

KW - dipolar diatomics

KW - phase-diagrams

KW - thermodynamics

KW - solvation

KW - formalism

KW - liquids

UR - http://link.aip.org/link/?JCP/102/5460/1

U2 - 10.1063/1.469274

DO - 10.1063/1.469274

M3 - Article

VL - 102

SP - 5460

EP - 5470

JO - Journal of Chemical Physics

T2 - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 13

ER -