Analytical solutions of the proper integral-equations for interaction site fluids: molecules composed of hard-sphere interaction sites

L. Lue, D. Blankschtein

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

Interaction site models are used quite extensively to describe molecular fluids. However, theories for these fluids are not as well developed or tested as compared to those for simple fluids. With this in mind, it appears useful to develop analytical expressions for the thermodynamic properties of fluids whose molecules are composed of hard‐sphere interactions sites, since these systems can serve as a convenient reference state for perturbation theories for molecular fluids. In an effort to achieve this goal and advance our understanding of molecular fluids, in this paper, we present an analysis of the Chandler-Silbey-Ladanyi (CSL) equations, a diagrammatically proper set of integral equations for interaction site fluids, with the specific aim of solving them analytically. First, we rewrite the CSL equations to explicitly account for the presence of equivalent sites. We find that the mathematical structure of the resulting CSL equations remains the same as that of the original CSL equations, subject to slight modifications in some of the matrices which appear in these equations. Subsequently, we apply the Wiener-Hopf factorization technique to the CSL equations with the Percus-Yevick (PY) closure for a general fluid composed of hard‐sphere interaction sites. We then analytically solve these equations for symmetric n‐atomic tangent hard‐sphere molecules (n≤4: spheres, diatomics, triangles, and tetrahedrals), which results in analytical expressions for the equation of state and other thermodynamic properties of the fluid. Finally, we compare the predictions of the analytical equation of state with those of other theories as well as with those of Monte Carlo simulations of these systems. The CSL equations with the PY closure are found to provide fair predictions for the equation of state of the fluids under investigation. More specifically, the CSL-PY equations tend to perform better for smaller molecules and at lower densities.
LanguageEnglish
Pages7086-7097
Number of pages11
JournalJournal of Chemical Physics
Volume103
Issue number16
DOIs
Publication statusPublished - 22 Oct 1995

Fingerprint

Integral equations
integral equations
Molecules
Fluids
fluids
molecules
interactions
Equations of state
equations of state
closures
Thermodynamic properties
thermodynamic properties
predictions
Factorization
tangents
factorization
triangles
perturbation theory
matrices

Keywords

  • directional attractive forces
  • thermodynamic perturbation- theory
  • asymmetric electrolytes
  • classical fluids
  • chain molecules
  • state
  • model
  • mixtures
  • polymerization
  • equilibria

Cite this

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title = "Analytical solutions of the proper integral-equations for interaction site fluids: molecules composed of hard-sphere interaction sites",
abstract = "Interaction site models are used quite extensively to describe molecular fluids. However, theories for these fluids are not as well developed or tested as compared to those for simple fluids. With this in mind, it appears useful to develop analytical expressions for the thermodynamic properties of fluids whose molecules are composed of hard‐sphere interactions sites, since these systems can serve as a convenient reference state for perturbation theories for molecular fluids. In an effort to achieve this goal and advance our understanding of molecular fluids, in this paper, we present an analysis of the Chandler-Silbey-Ladanyi (CSL) equations, a diagrammatically proper set of integral equations for interaction site fluids, with the specific aim of solving them analytically. First, we rewrite the CSL equations to explicitly account for the presence of equivalent sites. We find that the mathematical structure of the resulting CSL equations remains the same as that of the original CSL equations, subject to slight modifications in some of the matrices which appear in these equations. Subsequently, we apply the Wiener-Hopf factorization technique to the CSL equations with the Percus-Yevick (PY) closure for a general fluid composed of hard‐sphere interaction sites. We then analytically solve these equations for symmetric n‐atomic tangent hard‐sphere molecules (n≤4: spheres, diatomics, triangles, and tetrahedrals), which results in analytical expressions for the equation of state and other thermodynamic properties of the fluid. Finally, we compare the predictions of the analytical equation of state with those of other theories as well as with those of Monte Carlo simulations of these systems. The CSL equations with the PY closure are found to provide fair predictions for the equation of state of the fluids under investigation. More specifically, the CSL-PY equations tend to perform better for smaller molecules and at lower densities.",
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Analytical solutions of the proper integral-equations for interaction site fluids: molecules composed of hard-sphere interaction sites. / Lue, L.; Blankschtein, D.

In: Journal of Chemical Physics, Vol. 103, No. 16, 22.10.1995, p. 7086-7097.

Research output: Contribution to journalArticle

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T1 - Analytical solutions of the proper integral-equations for interaction site fluids: molecules composed of hard-sphere interaction sites

AU - Lue, L.

AU - Blankschtein, D.

N1 - English Article TA441 J CHEM PHYS

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N2 - Interaction site models are used quite extensively to describe molecular fluids. However, theories for these fluids are not as well developed or tested as compared to those for simple fluids. With this in mind, it appears useful to develop analytical expressions for the thermodynamic properties of fluids whose molecules are composed of hard‐sphere interactions sites, since these systems can serve as a convenient reference state for perturbation theories for molecular fluids. In an effort to achieve this goal and advance our understanding of molecular fluids, in this paper, we present an analysis of the Chandler-Silbey-Ladanyi (CSL) equations, a diagrammatically proper set of integral equations for interaction site fluids, with the specific aim of solving them analytically. First, we rewrite the CSL equations to explicitly account for the presence of equivalent sites. We find that the mathematical structure of the resulting CSL equations remains the same as that of the original CSL equations, subject to slight modifications in some of the matrices which appear in these equations. Subsequently, we apply the Wiener-Hopf factorization technique to the CSL equations with the Percus-Yevick (PY) closure for a general fluid composed of hard‐sphere interaction sites. We then analytically solve these equations for symmetric n‐atomic tangent hard‐sphere molecules (n≤4: spheres, diatomics, triangles, and tetrahedrals), which results in analytical expressions for the equation of state and other thermodynamic properties of the fluid. Finally, we compare the predictions of the analytical equation of state with those of other theories as well as with those of Monte Carlo simulations of these systems. The CSL equations with the PY closure are found to provide fair predictions for the equation of state of the fluids under investigation. More specifically, the CSL-PY equations tend to perform better for smaller molecules and at lower densities.

AB - Interaction site models are used quite extensively to describe molecular fluids. However, theories for these fluids are not as well developed or tested as compared to those for simple fluids. With this in mind, it appears useful to develop analytical expressions for the thermodynamic properties of fluids whose molecules are composed of hard‐sphere interactions sites, since these systems can serve as a convenient reference state for perturbation theories for molecular fluids. In an effort to achieve this goal and advance our understanding of molecular fluids, in this paper, we present an analysis of the Chandler-Silbey-Ladanyi (CSL) equations, a diagrammatically proper set of integral equations for interaction site fluids, with the specific aim of solving them analytically. First, we rewrite the CSL equations to explicitly account for the presence of equivalent sites. We find that the mathematical structure of the resulting CSL equations remains the same as that of the original CSL equations, subject to slight modifications in some of the matrices which appear in these equations. Subsequently, we apply the Wiener-Hopf factorization technique to the CSL equations with the Percus-Yevick (PY) closure for a general fluid composed of hard‐sphere interaction sites. We then analytically solve these equations for symmetric n‐atomic tangent hard‐sphere molecules (n≤4: spheres, diatomics, triangles, and tetrahedrals), which results in analytical expressions for the equation of state and other thermodynamic properties of the fluid. Finally, we compare the predictions of the analytical equation of state with those of other theories as well as with those of Monte Carlo simulations of these systems. The CSL equations with the PY closure are found to provide fair predictions for the equation of state of the fluids under investigation. More specifically, the CSL-PY equations tend to perform better for smaller molecules and at lower densities.

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KW - thermodynamic perturbation- theory

KW - asymmetric electrolytes

KW - classical fluids

KW - chain molecules

KW - state

KW - model

KW - mixtures

KW - polymerization

KW - equilibria

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DO - 10.1063/1.470337

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EP - 7097

JO - Journal of Chemical Physics

T2 - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 16

ER -