Electrical potentials of two identical particles with fixed surface charge density in a salt-free medium

The electrical potentials of two identical planar, cylindrical, and spherical particles immersed in a salt-free dispersion are solved analytically by a perturbation approach for the case of constant surface charge density. The system under consideration simulates, for example, micelles, where the ionic species in the liquid phase come mainly from the dissociation of the functional groups on the droplet surface. We show that for planar particles, the present zero-order perturbation solution is exact, and for cylindrical and spherical particles, the first-order perturbation solution provides sufficiently accurate results, with an averaged percentage deviation on the order of 1% under typical conditions. In general, the higher the surface charge density, the higher the valence of counterions, the smaller the separation distance between two particles, and the smaller the curvature of particle surface, the better the performance of the perturbation solution.

Graphical abstractElectrical distribution for the case of two charged particles in a salt-free medium.Figure optionsDownload full-size imageDownload high-quality image (138 K)Download as PowerPoint slideResearch highlights► Problem considered simulates a wide class of colloidal systems including micelles. ► Electrical potentials of two planar and nonplanar particles are derived. ► Accurate approximate analytical expressions are obtained. ► Results are readily applicable to the evaluation of electrical energy.