A semi-analytical calculation of the electrostatic pair interaction between nonuniformly charged colloidal spheres at...

We study the electrostatic pair interaction between two nonuniformly like-charged colloidal spheres trapped in an air-water interface. Under the linear Poisson-Boltzmann approximation, a general form of the electrostatic potential for the system is shown in terms of multipole expansions. After combining the translation-rotation transform of the coordinates with the numerical multipoint collection, we give a semi-analytical result of the electrostatic pair interaction between the colloids. The pair interaction changes quantitatively or even qualitatively with different distributions of the surface charges on the particles. Because of the anisotropic distribution of the surface charge and the asymmetric dielectric medium, the dipole moment of the ion cloud associating with the particle orients diagonally to the air-water interface with an angle α. When the angle is large, the colloids interact repulsively, while they attract each other when the angle is small. The attractive colloids may be "Janus-like" charged and be arranged with some specific configurations. Whatever the repulsions or the attractions, they all decay asymptotically ∝1/d(3) (d is the center-center distance of the particles) which is consistent with our general acknowledge. The calculation results also provide an insight of the effect of the ion concentration, particle size, and the total charge of the particle on the pair interaction between the particles.