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Electrophoresis of Spherical Particles with a Random Distribution of Zeta Potential or Surface Charge

Journal of Colloid and Interface Science
Publication Date
DOI: 10.1006/jcis.2000.7049
  • Charge Nonuniformity
  • Charge Heterogeneity
  • Random Charge
  • Patchy Sphere
  • Electrophoresis
  • Electrophoretic Rotation


Abstract Electrophoresis is often used to measure the “average” zeta (ζ) potential on particles. However, it has been found by previous researchers that in making predictions of colloidal forces and stability, the distribution of ζ potential on the particles is important. This paper provides a straightforward method for measuring charge nonuniformity on colloidal spheres. It is shown that if the charge or ζ potential is random on a group of spheres, each covered with N equal-area patches, then the average magnitude of the dipole moment on the spheres is 0.92σζ/N, and the average magnitude of the quadrupole moment is 1.302σζ/N, where σζ is the standard deviation of ζ potential over the surface of individual spheres. This is true for any random distribution of ζ potential, and the results emphasize that “random” implies nonuniform. It is demonstrated that since typical translational mobility measurements are much less sensitive to random charge nonuniformity than rotational mobility measurements, the latter measurement is better suited for measuring the second moment (σζ) of ζ potential. Monte Carlo simulations were done to confirm and extend the analytical results.

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