Modified Poisson–Boltzmann theory for polyelectrolytes in monovalent salt solutions with finite-size ions

Nonmonotonic electrophoretic mobility of rodlike polyelectrolytes by multivalent coions in added salt

It is well established that when multivalent counterions or salts are added to a solution of highly charged polyelectrolytes (PEs), correlation effects can cause charge inversion of the PE, leading to electrophoretic mobility (EM) reversal. In this work, we use coarse-grained molecular-dynamics simulations to unravel the less understood effect of coion valency on EM reversal for rigid DNA-like PEs. We find that EM reversal induced by multivalent counterions is suppressed with increasing coion valency in the salt added and eventually vanishes. Further, we find that EM is enhanced at fixed low salt concentrations for salts with monovalent counterions when multivalent coions with increasing valency are introduced. However, increasing the salt concentration causes a crossover that leads to EM reversal which is enhanced by increasing coion valency at high salt concentration. Remarkably, this multivalent coion-induced EM reversal persists even for low values of PE linear charge densities where multivalent counterions alone cannot induce EM reversal. These results facilitate tuning PE-PE interactions and self-assembly with both coion and counterion valencies.

Interactions between Rigid Polyelectrolytes Mediated by Ordering and Orientation of Multivalent Nonspherical Ions in Salt Solutions

Multivalent ions in solutions with polyelectrolytes (PEs) induce electrostatic correlations that can drastically change ion distributions around the PEs and their mutual interactions. Using coarse-grained molecular dynamics simulations, we show how in addition to valency, ion shape and concentration can be harnessed as tools to control rigid like-charged PE-PE interactions. We demonstrate a correlation between the orientational ordering of aspherical ions and how they mediate the effective PE-PE attraction induced by multivalency. The interaction type, strength, and range can thus be externally controlled in ionic solutions. Our results can be used as generic guidelines to tune the self-assembly of like-charged polyelectrolytes by variation of the characteristics of the ions.

Theoretical and computational analysis of the electrophoretic polymer mobility inversion induced by charge correlations

Electrophoretic (EP) mobility reversal is commonly observed for strongly charged macromolecules in multivalent salt solutions. This curious effect takes place, e.g., when a charged polymer, such as DNA, adsorbs excess counterions so that the counterion-dressed surface charge reverses its sign, leading to the inversion of the polymer drift driven by an external electric field. In order to characterize this seemingly counterintuitive phenomenon that cannot be captured by electrostatic mean-field theories, we adapt here a previously developed strong-coupling-dressed Poisson-Boltzmann approach to the cylindrical geometry of the polyelectrolyte-salt system. Within the framework of this formalism, we derive an analytical polymer mobility formula dressed by charge correlations. In qualitative agreement with polymer transport experiments, this mobility formula predicts that the increment of the monovalent salt, the decrease of the multivalent counterion valency, and the increase of the dielectric permittivity of the background solvent suppress charge correlations and increase the multivalent bulk counterion concentration required for EP mobility reversal. These results are corroborated by coarse-grained molecular dynamics simulations showing how multivalent counterions induce mobility inversion at dilute concentrations and suppress the inversion effect at large concentrations. This re-entrant behavior, previously observed in the aggregation of like-charged polymer solutions, calls for verification by polymer transport experiments.

Interaction between two polyelectrolytes in monovalent aqueous salt solutions

We use the recently developed soft-potential-enhanced Poisson-Boltzmann (SPB) theory to study the interaction between two parallel polyelectrolytes (PEs) in monovalent ionic solutions in the weak-coupling regime. The SPB theory is fitted to ion distributions from coarse-grained molecular dynamics (MD) simulations and benchmarked against all-atom MD modelling for poly(diallyldimethylammonium) (PDADMA). We show that the SPB theory is able to accurately capture the interactions between two PEs at distances beyond the PE radius. For PDADMA positional correlations between the charged groups lead to locally asymmetric PE charge and ion distributions. This gives rise to small deviations from the SPB prediction that appear as short-range oscillations in the potential of mean force. Our results suggest that the SPB theory can be an efficient way to model interactions in chemically specific complex PE systems.