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

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

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Article number121073
JournalJournal of Molecular Liquids
Early online date16 Dec 2022
Publication statusPublished - 1 Feb 2023


  • 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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