Phase diagram of solution of oppositely charged polyelectrolytes

TL;DR

This paper explores the phase behavior of oppositely charged polyelectrolyte solutions, revealing how charge ratios and screening influence complex formation, leading to various phases including neutral, condensed, and tadpole-like structures.

Contribution

It provides a detailed phase diagram of polyelectrolyte solutions considering Coulomb interactions and disproportionation mechanisms, a novel comprehensive analysis.

Findings

Neutral complexes condense at charge ratio x=1

Charged complexes remain stable when x is far from 1

Phase coexistence includes neutral, charged, and tadpole phases

Abstract

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.