  We study a solution of long polyanions (PA) with shorter polycations (PC) and
focus on the role of Coulomb interaction. A good example is solutions of DNA
and PC which are widely studied for gene therapy. In the solution, each PA
attracts many PCs to form a complex. When the ratio of total charges of PA and
PC in the solution, $x$, equals to 1, complexes are neutral and they condense
in a macroscopic drop. When $x$ is far away from 1, complexes are strongly
charged. The Coulomb repulsion is large and free complexes are stable. As $x$
approaches to 1, PCs attached to PA disproportionate themselves in two
competing ways. One way is inter-complex disproportionation, in which PCs make
some complexes neutral and therefore condensed in a macroscopic drop while
other complexes become even stronger charged and stay free. The other way is
intra-complex disproportionation, in which PCs make one end of a complex
neutral and condensed in a small droplet while the rest of the complex forms a
strongly charged tail. Thus each complex becomes a "tadpole". These two ways
can also combine together to give even lower free energy. We get a phase
diagram of PA-PC solution in a plane of $x$ and inverse screening radius of the
monovalent salt, which includes phases or phase coexistence with both kinds of
disproportionation.
