  The formation of inter-polyelectrolyte complexes from the association of
oppositely charged polymers in an electrolyte is studied. The charged polymers
are linear oppositely charged polyelectrolytes, with possibly a neutral block.
This leads to complexes with a charged core, and a more dilute corona of
dangling chains, or of loops (flower-like structure). The equilibrium
aggregation number of the complexes (number of polycations m+ and polyanions
m-) is determined by minimizing the relevant free energy functional, the
Coulombic contribution of which is worked out within Poisson-Boltzmann theory.
The complexes can be viewed as colloids that are permeable to micro-ionic
species, including salt. We find that the complexation process can be highly
specific, giving rise to very localized size distribution in composition space
(m+,m-).
