Multipole expansion of the electrostatic interaction between charged colloids at interfaces
A. Dom\'{\i}nguez, D. Frydel, and M. Oettel

The general form of the electrostatic potential around an arbitrarily charged colloid at a flat interface between a dielectric and a screening phase (such as air and water, respectively) is analyzed in terms of a multipole expansion. The leading term is isotropic in the interfacial plane and varies with $d^{-3}$ where $d$ is the in--plane distance from the colloid. The effective interaction potential between two arbitrarily charged colloids is likewise isotropic and $\propto d^{-3}$, thus generalizing the dipole--dipole repulsion first found for point charges at water interfaces. Anisotropic, attractive interaction terms can arise only for higher powers $d^{-n}$ with $n \ge 4$. The relevance of these findings for recent experiments is discussed.

© 2008 The American Physical Society.