Physics underlying controlled self-assembly of micro- and nanoparticles at a two-fluid interface using an electric field

The purpose of this paper is to investigate the physics underlying the controlled self-assembly of microparticles and nanoparticles at a two-fluid interface using an electric field. As shown in recent experiments, under certain conditions an externally applied electric field can cause particles floating at a two-fluid interface to assemble into a virtually defect free monolayer whose lattice spacing can be adjusted by varying the electric field strength. In this work, we assume that both fluids and particles are perfect dielectrics and for this case analyze the (capillary and electrical) forces acting on the particles, deduce an expression for the lattice spacing under equilibrium condition, and study the dependence of the latter upon the various parameters of the system, including the particles' radius, the dielectric properties of the fluids and particles, the particles' position within the interface, the particles' buoyant weight, and the applied voltage. While for relatively large sized particles whose buoyant weight is much larger than the vertical electrostatic force, the equilibrium distance increases with increasing electric field, for submicron sized particles whose buoyant weight is negligible, it decreases with increasing electric field. For intermediate sized particles, the distance first increases and then decreases with increasing electric field strength.