Free Energy Profile of Complexation of two oppositely charged Polyelectrolytes*

We report a study of the complexation process of two oppositely charged polyelectrolyte (PE) chains in dilute solution interacting through screened Coulomb potential within the DLVO framework. 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, and the system is characterized by its free energy, calculated within the uniform spherical expansion approximation. Detailed comparative study of the effect of entropy gain of free counterions due to complexation and enthalpy change due to the reorganization of ion-pairs into two types-both of the monomer-counterion type and oppositely charged monomer-monomer type is shown. We have looked into both salt-free and salty conditions and how it affects the complex formation process. Several factors drive the mutual adsorption of the two PEs to form a neutral coacervate. The full free energy profile of complexation, including the intermediate stages, is found to be monotonic at all conditions. A free energy landscape for the pathway of the complexation process may also be employed in studying the quantitative time scales in the kinetics of complex coacervation of two PEs.