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An Expression for the Dispersion Force between Colloidal Particles

Henderson1, Duh, Chu

  • 1Department of Chemistry and Biochemistry, Brigham Young University, Provo, Utah, 84602

Journal of Colloid and Interface Science
|January 1, 1997
PubMed
Summary
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Researchers derived an integral for R-12 over spheres, aiding calculations for colloidal particles. This, with Hamaker

Area of Science:

  • Colloid and Surface Science
  • Physical Chemistry
  • Mathematical Physics

Background:

  • The Lennard-Jones potential is crucial for modeling interactions between colloidal particles.
  • Calculating integrals of interaction potentials over particle geometries is computationally intensive.
  • Existing solutions for R-6 interactions are available, but R-12 requires specific derivation.

Purpose of the Study:

  • To derive a general result for the integral of R-12 over two spheres.
  • To combine this with existing R-6 integral results to form a complete Lennard-Jones potential integral.
  • To provide a computationally suitable expression for colloidal particle interaction calculations.

Main Methods:

  • Analytical integration of the R-12 term over spherical surfaces.

Related Experiment Videos

  • Leveraging Hamaker's established integral for the R-6 term.
  • Combining derived and existing results to form the complete Lennard-Jones potential integral.

    • Main Results:

    • A specific mathematical result for the integral of R-12 over two spheres of radii a and b.
    • A comprehensive expression for the integral of the Lennard-Jones potential over two spheres.
    • The derived expression is optimized for practical application in colloidal systems.

    Conclusions:

    • The study provides a key mathematical tool for understanding colloidal interactions.
    • The derived integral simplifies complex calculations involving the Lennard-Jones potential.
    • This work facilitates more accurate modeling and prediction of behavior in colloidal dispersions.