Dipole Moment of a Charged Particle Trapped at the Air-Water Interface

The interaction between two charged particles (such as nanoparticles or colloids) trapped at the air-water interface becomes dipolar at large separations. The corresponding dipole moment can be modeled by considering a single point charge located exactly at the interface, but this model fails to correctly predict the dipole moment's dependence on the salt concentration in the aqueous medium. We extend the single point charge model to two point charges that are separated by a fixed distance and are located at the air-water interface, with one charge being immersed in air and the other in the solvent. The two point charges represent the surface charges at the air-exposed and water-exposed regions of an interface-trapped particle. The two point charges also account for the spatial extension of the particle. On the basis of the Debye-Hückel model, we derive mathematical expressions for the interaction between two pairs of charges and discuss the salt concentration dependence of the dipolar moment at large separations. Our results reveal a residual dipole moment in the limit of large salt content that originates from the charge attached to the air-exposed region of the particle. We discuss nonlinear screening effects and compare the predicted dipolar moments with recent experimental results.