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". We get a phase diagram of PA-PC solution in a plane of x and the inverse screening radius of the monovalent salt, which includes phases with both kinds of disproportionation.
|Original language||English (US)|
|Number of pages||23|
|Journal||Physica A: Statistical Mechanics and its Applications|
|State||Published - Jul 1 2005|
Bibliographical noteFunding Information:
The authors are grateful to V. Budker, A. Yu. Grosberg, and M. Rubinstein for useful discussions. This work was supported by NSF No. DMR-9985785 and DMI-0210844.