The double-layer interaction of two charged colloidal spherical particles of a concentrated dispersion in a medium of low dielectric constant: III. Approximation of perfectly conducting particles

Abstract

We investigate the electric double-layer force between two neighboring, charged identical, spherical colloidal particles O 1 and O 2 of a concentrated dispersion in a hydrocarbon medium. Only one ionic species, constituting the counterion, is present in the hydrocarbon, and this is at such a low concentration that its mean volume density is virtually uniform. To account for the surrounding particles of the dispersion, it is imagined that O 1 and O 2 are enclosed by a symmetrical surface S 0 such that the net charge contained by S 0 is zero. The volume contained by S 0 equals twice the volume per particle, and S 0 can be chosen so that the normal derivative of the potential on S 0 is zero. The potential distribution in the hydrocarbon medium is governed by Poisson's equation and a solution of this equation is obtained as an infinite series expressed in terms of bispherical coordinates. For simplicity, the surfaces of the two particles are assumed to be equipotentials with fixed total surface charge. A general expression for the double layer force is given as an integral involving the Maxwell electrostatic stress and the osmotic pressure. First and second approximations to this force show that at the mean separation between neighboring particles, the double-layer force is attractive, and it is concluded that double-layer effects alone will not stabilize a highly concentrated suspension in a hydrocarbon medium.