  Despite decades of intensive studies, the effective interactions between
strongly charged colloids still remain elusive. Here we show that a strongly
charged surface with a layer of condensed counter- ions behaves effectively as
a conductor, due to the mobile nature of the condensed ions. An external source
charge in its vicinity is therefore attracted towards the surface, due to the
image charge effect. This mechanism leads to correlational energies for
counter-ions condensed on two distinct surfaces, as well as for free ions in
the bulk. Generalizing Debye-Huckel theory and image charge methods, we
analytically calculate these correlation energies for the two-plates problem,
at the iso-electric point, where condensed counterions precisely balance the
bare surface charges. At this point, the effective interaction between two
plates is always attractive at small separation and repulsive at large
separation.
