Entropy-DrivenAttraction between Weakly Basic PolyelectrolytesIonized with Monoprotic Acids

Under suitable solution conditions, polyelectrolytes can form self-organized structures. Self-assembly of oppositely charged polyelectrolytes in aqueous solutions occurs due to electrostatic attractions and the increased entropy of the released counterions and water molecules. Like-charged polyelectrolytes are commonly reported to self-assemble with the help of multivalent counterions through ion bridging between the chains. Monovalent counterions are not expected to facilitate a strong association between like-charged polyelectrolytes. However, it has recently been demonstrated that cationic polyethylenimine (PEI) self-assembles into hollow fibrils in moderately acidic aqueous solutions when protonated with monobasic acids. This phenomenon cannot be explained by electrostatic screening alone and is not yet fully understood. Since most applications of PEI, including its use as a transfection reagent, occur in acidic environments, it is important to understand what leads to such unique self-association and the underlying molecular-level mechanisms. With this objective, we use all-atom molecular dynamics to estimate the potential of mean force (PMF) between a pair of polyethylenimine oligomers in aqueous solution protonated with hydrochloric acid. The PMF exhibits an interesting nonmonotonic progression of interactions with change in protonation fraction, and peculiarly, a strong attraction window is seen at moderately high protonation fractions. This is in close agreement with previously reported experiments. Interestingly, the net sum of bonded and nonbonded interactions between the chains remains repulsive, indicating that such assembly may be entropically driven. This is also confirmed by the decrease in PMF with the temperature. The attraction window coincides with a significant increase in the fraction of counterions present around two proximal polymer chains. The role of various interactions between the chains, counterions, solvent molecules, and the variation of polymer conformations are studied. These simulations depict some of the molecular mechanisms at play during the association of like-charged polyelectrolytes and advance our understanding of polyelectrolyte self-assembly.