The role of multipoles in counterion-mediated interactions between charged surfaces: strongand weak coupling

Abstract

We present general arguments for the importance, or lack thereof, of structure in the chargedistribution of counterions for counterion-mediated interactions between boundingsymmetrically charged surfaces. We show that on the mean field or weak coupling level, thecharge quadrupole contributes the lowest order modification to the contact valuetheorem and thus to the intersurface electrostatic interactions. The image effects arenon-existent on the mean field level even with multipoles. On the strong coupling levelthe quadrupoles and higher order multipoles contribute additional terms to theinteraction free energy only in the presence of dielectric inhomogeneities. Withoutthem, the monopole is the only multipole that contributes to the strong couplingelectrostatics. We explore the consequences of these statements in all their generality.