Forces acting on dielectric colloidal spheres at a water/nonpolar fluid interface in an external electric field. 2. Charged particles.

Here, we calculate the electric forces acting on charged dielectric colloidal particles, which are attached to the interface between a nonpolar fluid (air and oil) and water in the presence of applied uniform external electric field, E0, directed normal to the interface. Electric charges are present on the particle-nonpolar fluid interface. The solution to the problem represents a superposition of the solutions of two simpler problems: (i) charged particle in the absence of external field and (ii) uncharged particle in the presence of external field. Because the external field can be directed upward or downward, it enhances or opposes the effect of the particle surface charges. As a result, the vertical (electrodipping) force vs. E0 may have a maximum or minimum and can be positive or negative depending on the particle contact angle and dielectric constant. In contrast, the lateral electric force between two identical charged floating particles is always positive (repulsive), but it can vary by many orders of magnitude with E0. This is because at a certain value of E0, the net dipolar moment of the particle becomes zero. Then, the interparticle force is governed by the octupolar moment, which leads to a much weaker and short-range repulsion. In the vicinity of this special value of E0, the interparticle repulsion is very sensitive to the variations in the external field. These effects can be used for a fine control of the lattice spacing in non-densely packed interfacial colloidal crystals of regular hexagonal packing for producing lithographic masks with various applications in nanotechnology.