The free energy profile of complexation of two oppositely charged polyelectrolyte chains

We report a study of the complexation process of two oppositely charged polyelectrolyte (PE) chains in dilute solution interacting through an attractive screened Coulomb potential. The system is modeled using the PE chain free energy within the uniform spherical expansion approximation where the two PE chains as well as the neutral complex are considered to be hypothetical spheres whose radii quantitatively denote the sizes of the respective chains. The two chains start overlapping due to attraction between the monomers, as well as the entropy gain of free counterions. The complexation process ends up in the formation of a neutral coecervate through mutual adsorption of oppositely charged monomers, with associated release of all counterions of both types. The free energy profile that follows this pathway is studied by obtaining the variations of the total free energy, as well as the various individual energy and entropy contributions, as functions of the extent of overlap of the two chains. Also the behavior of the chain size and charge as functions of overlap is presented. These results elucidate the competition of the various driving forces, both enthalpic and entropic in nature, which lead to complexation.