Multipolar expansion of the electrostatic interaction between charged colloids at interfaces

Dominguez, A.; Frydel, D.; Oettel, M.

Multipolar expansion of the electrostatic interaction between charged colloids at interfaces

Authors

Dominguez, A.

Frydel, D.

Oettel, M.

Description

The general form of the electrostatic potential around an arbitrarily charged colloid at an 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 electrostatic interaction potential between two arbitrarily charged colloids is likewise isotropic and $\propto d^{-3}$, corresponding to the dipole--dipole interaction first found for point charges at water interfaces. Anisotropic interaction terms arise only for higher powers $d^{-n}$ with $n \ge 4$.
6 pages, mathematical details added