Abstract
Approximate analytic expressions of the surface charge density/surface potential relationship and double-layer potential distribution are derived for a spherical colloidal particle in 1-1 and 2-1 electrolyte solutions and a mixed 1-1 and 2-1 electrolyte solution. These expressions are shown to be excellent approximations to the exact numerical values obtained by Loeb, Overbeek, and Wiersema (“The Electrical Double Layer Around a Spherical Colloidal Particle.” MIT Press, Cambridge, Mass., 1961) over a wide range of ϰ a values (ϰ = Debye-Hückel parameter and a = particle radius) for all values of the surface potential and are considerably better approximations than those obtained previously by White ( J. Chem. Soc. Faraday Trans. 2 73, 577 (1977)). The mathematical basis for an empirical surface charge density/surface potential relationship for 1-1 electrolytes quoted by Loeb et al. is ellucidated. The method is extended to the case of a cylinder in 1-1 electrolyte. In addition, a more accurate expression for the interaction energy of two spherical colloidal particles at large distance is also derived.
Published Version
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