Phase diagram of solution of oppositely charged polyelectrolytes

Rui Zhang, B. I. Shklovskii

Research output: Contribution to journalArticlepeer-review

133 Scopus citations


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 languageEnglish (US)
Pages (from-to)216-238
Number of pages23
JournalPhysica A: Statistical Mechanics and its Applications
Issue number1
StatePublished - Jul 1 2005

Bibliographical note

Funding 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.


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