Long-range attraction between likely charged colloidal particles as a consequence of collective effects

A dynamic screening of the Coulomb potential of a moving negatively charged colloidal particle was studied based on the Vlasov kinetic equation containing the collision operator in its right-hand side in conjunction with the Poisson equation for positively charged counterions. The screened potential is dependent on the velocity of the test colloidal particle and the dynamic dielectric susceptibility of the system. Since actual colloidal particles execute Brownian motions, the screened potential was calculated by averaging the screened potential of the test particle over the Maxwellian velocity distribution. The effective (renormalized) potential of the charged colloidal particle decreases faster then the Debye Huckel potential and has a negative part that may cause the attraction between similarly charged colloidal particles. Since the intensity of the Brownian motion of colloidal particles of moderate mass is rather high, the attractive minimum of the renormalized potential is deep enough to ensure the crystallization of colloidal particles, an effect that was observed experimentally [1]. The distance from the minimum of the potential well to the center of the spherical colloidal particle was found to coincide with the period of the lattice in the crystallites formed.