(59f) Model of Equilibrium over-Charging in Polyelectrolyte Complexes

Intuitively, one may expect polyelectrolyte complexes (PECs) made from solutions of oppositely-charged polyelectrolytes to be neutral at equilibrium; however, for solutions with non-equimolar polyanion and polycation concentrations, one can produce overcharged PECs. Overcharging is a ubiquitous, yet poorly understood, phenomenon for both natural and synthetic polyelectrolytes. Formation of nucleosomes by DNA-histone complexation, encapsulation of large lengths of genome inside viral capsids, formation of layer-by-layer (LbL) films, and creating positively-charged DNA-cationic lipid complexes for gene delivery are just a few famous examples of overcharged PECs. Here, using a solution free energy, which incorporates long-ranged electrostatic interactions, ion-specific interactions, and chain connectivity, we perform a parametric study of overcharging of PECs under varying conditions to understand thermodynamics of this phenomenon and delineate the underlying driving forces for overcharging of PECs. We find distinctive regimes of over-charging, governed by the strengths of the binding of polymeric and small-ion species to oppositely charged polymers, and by translational and combinatorial entropy of free and bound species, respectively. We compare the predictions of our theory to experimental results of Schlenoff and coworkers as a function of salt concentration and find fits using ion binding strengths as adjustable parameters. The results indicate that such “overcharging” experiments can be used to assess the strengths of binding of small ions to oppositely charged polymers. Correct prediction of overcharging is a first step towards prediction of the thermodynamics and eventually kinetics of growth of Layer-by-Layer films.