Integral equation theory for a valence-limited model of colloidal systems

Y. V. Kalyuzhnyi; A. Jamnik; P. T. Cummings

doi:10.1016/j.molliq.2022.121073

Integral equation theory for a valence-limited model of colloidal systems

Y. V. Kalyuzhnyi, A. Jamnik, P. T. Cummings

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

An analytic theory for the structure and thermodynamics of the Speedy-Debenedetti-Baxter valence-limited model of colloidal fluids is developed. It is based on the solution of the multidensity version of the Ornstein–Zernike equation supplemented by a Percus–Yevick-like closure relation, which are formulated for systems with a central-force type of associating potential. Our solution is reduced to the solution of a set of two algebraic equations for the fractions of free and singly bonded particles. We derive analytic expressions for the correlation functions, structure factor and excess internal energy of the model. The accuracy of the theoretical predictions is assessed through their comparison against existing and newly generated computer simulation results for the model with the valency n _s=2,3,4. Very good agreement between theoretical and computer simulation results is observed for the structural properties. Predictions for the fractions of i-times (i⩽n _s) bonded particles and for excess internal energy for the model with n _s=3,4 are slightly less accurate.

Original language	English
Article number	121073
Journal	Journal of Molecular Liquids
Volume	371
Early online date	16 Dec 2022
DOIs	https://doi.org/10.1016/j.molliq.2022.121073
Publication status	Published - 1 Feb 2023

Keywords

Association
Colloids
Integral equation theory
Limited valence
Multi-density
Percus–Yevick

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Atomic and Molecular Physics, and Optics
Condensed Matter Physics
Spectroscopy
Physical and Theoretical Chemistry
Materials Chemistry

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10.1016/j.molliq.2022.121073

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title = "Integral equation theory for a valence-limited model of colloidal systems",

abstract = "An analytic theory for the structure and thermodynamics of the Speedy-Debenedetti-Baxter valence-limited model of colloidal fluids is developed. It is based on the solution of the multidensity version of the Ornstein–Zernike equation supplemented by a Percus–Yevick-like closure relation, which are formulated for systems with a central-force type of associating potential. Our solution is reduced to the solution of a set of two algebraic equations for the fractions of free and singly bonded particles. We derive analytic expressions for the correlation functions, structure factor and excess internal energy of the model. The accuracy of the theoretical predictions is assessed through their comparison against existing and newly generated computer simulation results for the model with the valency n s=2,3,4. Very good agreement between theoretical and computer simulation results is observed for the structural properties. Predictions for the fractions of i-times (i⩽n s) bonded particles and for excess internal energy for the model with n s=3,4 are slightly less accurate.",

keywords = "Association, Colloids, Integral equation theory, Limited valence, Multi-density, Percus–Yevick",

author = "Kalyuzhnyi, {Y. V.} and A. Jamnik and Cummings, {P. T.}",

note = "Funding Information: A.J. thanks the financial support of the Slovenian Research Agency through the research core funding No. P1-0201. The authors dedicate this paper to the memory of Doug Henderson, who has been an inspiration in the field of fluid-state statistical mechanics for more than six decades. PTC particularly recalls that in 1979/80, Doug was one of the anonymous external readers of his PhD thesis at the University of Melbourne (Australia), which, after graduation, quickly led to a warm friendship that lasted many decades. Funding Information: A.J. thanks the financial support of the Slovenian Research Agency through the research core funding No. P1-0201. Publisher Copyright: {\textcopyright} 2022 Elsevier B.V.",

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N2 - An analytic theory for the structure and thermodynamics of the Speedy-Debenedetti-Baxter valence-limited model of colloidal fluids is developed. It is based on the solution of the multidensity version of the Ornstein–Zernike equation supplemented by a Percus–Yevick-like closure relation, which are formulated for systems with a central-force type of associating potential. Our solution is reduced to the solution of a set of two algebraic equations for the fractions of free and singly bonded particles. We derive analytic expressions for the correlation functions, structure factor and excess internal energy of the model. The accuracy of the theoretical predictions is assessed through their comparison against existing and newly generated computer simulation results for the model with the valency n s=2,3,4. Very good agreement between theoretical and computer simulation results is observed for the structural properties. Predictions for the fractions of i-times (i⩽n s) bonded particles and for excess internal energy for the model with n s=3,4 are slightly less accurate.

AB - An analytic theory for the structure and thermodynamics of the Speedy-Debenedetti-Baxter valence-limited model of colloidal fluids is developed. It is based on the solution of the multidensity version of the Ornstein–Zernike equation supplemented by a Percus–Yevick-like closure relation, which are formulated for systems with a central-force type of associating potential. Our solution is reduced to the solution of a set of two algebraic equations for the fractions of free and singly bonded particles. We derive analytic expressions for the correlation functions, structure factor and excess internal energy of the model. The accuracy of the theoretical predictions is assessed through their comparison against existing and newly generated computer simulation results for the model with the valency n s=2,3,4. Very good agreement between theoretical and computer simulation results is observed for the structural properties. Predictions for the fractions of i-times (i⩽n s) bonded particles and for excess internal energy for the model with n s=3,4 are slightly less accurate.

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KW - Limited valence

KW - Multi-density

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Integral equation theory for a valence-limited model of colloidal systems

Abstract

Keywords

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