Effective Surface Potential and Double-Layer Interaction of Colloidal Particles

Abstract

The double-layer interaction energy between two colloidal particles at large separations is proportional to the product of the scaled effective surface potentials of the respective particles (Bell et al., J. Colloid Interface Sci. 33, 335 (1970); Brenner, S. L., and Parsegian, V. A., Biophys. J. 14, 327 (1974)). The exact expression is obtained for the scaled effective surface potential of a plate in a solution of general electrolytes, which agrees with Wilemski's results (J. Colloid Interface Sci. 88, 111 (1982)). An accurate approximate analytic expression is derived for the scaled effective surface potential of a sphere in a solution of general electrolytes. For the special case of a sphere in a symmetrical electrolyte solution, the obtained expression reduces to that derived previously (Ohshima et al., J. Colloid Interface Sci. 90, 17 (1982)). The obtained expressions are found to be excellent approximations to the exact numerical values given by Loeb et al. ("The Electrical Double Layer Around a Spherical Colloidal Particle." MIT Press, Cambridge, MA, 1961), the relative error being less than 1% for κa > 1 (a = sphere radius and κ = Debye-Hückel parameter) at all values of the surface potential.