Image charge effects on colloidal crystal ordering

We theoretically investigated the effect of the container wall on the structural ordering of aqueous dispersions of negatively charged electrostatically stabilized colloidal spherical particles. The colloidal crystal contained between two quartz plates is modeled as a set of crystal planes oriented parallel to the quartz walls. We consider the electrostatic interactions between the particles and the container wall, and the particles and their induced image charges. The position-dependent interaction energies of a plane with its neighbors and the induced image charges are calculated under the Debye–Hückel approximation. We also theoretically investigate the effect of charged container walls on the ordering of the colloidal particle dispersion. For zero wall surface charge, the colloidal sphere plane nearest to the container wall is held in a deeper potential well than are interior colloidal planes. A negative wall surface charge creates a shallower well for the nearest colloidal sphere plane, which is still deeper than that of the interior planes. A positive wall surface charge creates the deepest potential well. These results rationalize our recent observations of the initial nucleation of crystalline colloidal array by formation of 2D hexagonal colloidal layers near the container wall. We calculate the root-mean-square displacement of the planes at various distances from the wall and use the Lindermann-type melting criteria to examine ordering.