Monovalent Counterions Research Articles

Counter-ion distribution around flexible polyelectrolytes having different molecular architecture.

We explore the monovalent counter-ion distribution around flexible highly-charged polyelectrolytes with different molecular architectures (linear chains, stars, and unknotted and trefoil rings) using molecular dynamics simulations that include an explicit solvent that interacts with the polyelectrolyte. In particular, we find that the molecular topology influences the fraction of counter-ions transiently associating with the polyelectrolyte on a scale of the order of the chain segments, forming a "condensed" counter-ion interfacial layer. As with the hydrogen bonding of water to proteins and other polymers, the persistence time of these interfacial "bound" counter-ions is relatively short, O(1 ps), and we characterize the fluctuations in the number of the counter-ions populating the interfacial layer. We also find that the counter-ions are distributed in a non-uniform fashion on the polyelectrolyte backbone, forming dynamical clusters whose form and average size is sensitive to molecular architecture. In addition, we find that the residual bound counter-ions, not located in either the interfacial layer or the bulk solution, form a diffuse ionic cloud around the polyelectrolyte due to the uncompensated polyelectrolyte charge along the backbone. Generally charge valence strongly influences the extent of the diffuse counter-ion cloud, but in the case of monovalent counter-ions, we find that the size of the diffuse counter-ion cloud nearly coincides with the polyelectrolyte radius of gyration, independent of molecular topology.

Specific effects of monovalent counterions on the structural and interfacial properties of dodecyl sulfate monolayers.

A series of molecular dynamics simulations have been conducted in order to study the specific ion effects of Li+, Na+, Cs+ and NH4+ cations on dodecyl sulfate (DS-) monolayers. Varying the counterion had no appreciable effect on the structure of the surfactant molecules within the different monolayers. However, the different counterions have a significant effect on the interfacial properties of the monolayer. In particular, we have investigated to what extent each of the counterions is dehydrated when interacting with the DS- headgroup, the specific interactions between the counterions and the headgroup and the salt bridging of the headgroups caused by each counterion. The NH4+ ions are found to directly compete with water molecules to form hydrogen bonds with the DS- headgroup and as a result the ammonium dodecyl sulfate monolayer is the least hydrated of any of those studied. The Cs+ ions are strongly bound to the headgroup and weakly hydrated, such that they would prefer to displace water in the DS- hydration shell to interact with the headgroups. In the case of the Li+ ions, they interact almost as strongly with the DS- headgroups as the Na+ ions, but are generally less hydrated than the Na+ ions and consequently the lithium dodecyl sulfate monolayers are less hydrated than the sodium dodecyl sulfate monolayers. Therefore, by changing the counterion, one can modify the interfacial properties of the surfactant monolayer, and thus affect their ability to encapsulate poorly water soluble drug molecules, which we discuss further in the manuscript.

The non-dominance of counterions in charge-asymmetric electrolytes: non-monotonic precedence of electrostatic screening and local inversion of the electric field by multivalent coions.

The asymptotic convergence of the thermodynamic and structural properties of unequally-sized charge-symmetric ions in strong electric fields was postulated more than thirty years ago by Valleau and Torrie as the dominance of counterions via the non-linear Poisson-Boltzmann theory [Valleau and Torrie, J. Chem. Phys., 1982, 76, 4623]. According to this mean field prescription, the properties of the electrical double layer near a highly charged electrode immersed in a size-asymmetric binary electrolyte converge to those of a size-symmetric electrolyte if the properties of counterions are the same in both instances. On the other hand, some of the present authors have shown that, in fact, counterions do not dominate the electrical properties of a spherical macroion in the presence of unequally-sized ions, symmetric in valence, if ion correlations and ionic excluded volume effects are taken into account consistently. These ingredients are neglected in the classical Poisson-Boltzmann picture. In the present work, we show the occurrence of the non-dominance of counterions in the opposite scenario, that is, when ions are equally-sized but asymmetric in valence. This is performed in the presence of highly charged colloidal surfaces of spherical and planar geometries for different ionic volume fractions. In addition to the phenomenon of non-dominance of counterions, our simulations and theoretical data also exhibit a non-monotonic order or precedence in the mean electrostatic potential, or electrostatic screening, at the Helmholtz plane of a charged colloid. This interesting behaviour is analyzed as a function of the coion's valence, the ionic volume fraction, and the charge and size of the colloidal particle. All these phenomena are explained in terms of the decay of the electric field near the colloidal surface, and by the appearance of a local inversion of both the electric field and the integrated surface charge density of the colloidal particle in the presence of monovalent counterions and multivalent coions.

Suppression and promotion of charge inversion in the presence of multivalent coions.

We report charge inversion using Monte Carlo calculations for a negatively charged surface in aqueous solutions involving coions of different charges and monovalent counterions. It is shown that a rise in the valence of coions at moderate concentrations can substantially promote charge inversion for the surface charge values of biological relevance, regardless of the representation of surface charges but dependent in a nontrivial way on polarization effects resulting from dielectric discontinuity. These obtained characteristics challenge the traditional belief that the coions are generally considered to suppress charge inversion and expose the important role of coions of higher valence in tailoring the effective interactions of biomolecules with the cell membrane.

Electrostatic potential of mean force between two curved surfaces in the presence of counterion connectivity.

In this paper, we investigate effects of counterion connectivity (i.e., association of the counterions into a chain molecule) on the electrostatic potential of mean force (EPMF) between two similarly charged cylinder rods in a primitive model electrolyte solution by solving a classical density functional theory. The main findings include the following: (i) The counterion connectivity helps in inducing a like-charge-attractionlike (LCA-like) phenomenology even in a monovalent counterion solution wherein the LCA-like observation generally does not occur without the counterion connectivity. (ii) For divalent counterion solutions, the counterion connectivity can reinforce or weaken the LCA-like observation depending on the chain length N, and simply increases the equilibrium nearest surface separation of the rods corresponding to the minimum EPMF to nearly three times the counterion site diameter, whether N is large or small. (iii) If N is large enough, the LCA-like strength tends to be negatively correlated with the electrolyte concentration c over the entire range of the rod surface charge magnitude |σ*| considered; whereas if N drops, the correlation tends to become positive with decrease of the |σ*| value, and particularly for modest |σ*| values, the correlation relationship exhibits an extreme value phenomenon. (iv) In the case of a 1:1 electrolyte, the EPMF effects of the diameters of counterion and coion sites are similar in both situations with and without the counterion connectivity. All of these findings can be explained self-consistently by a recently proposed hydrogen-bonding style mechanism reinforced by one additional concept: flexibility of the counterion chain and the factors affecting it, like N and counterion site valence.

Supramolecular Assembly of Poly(propyleneimine) Dendrimers Driven By Simple Monovalent Counterions.

The self-assembly of semiglobular, positively charged poly(propyleneimine) (PPI) dendrimers with small monovalent counterions (e.g., Cl(-)) in water/acetone mixtures was investigated. We showed that PPI dendrimers can assemble into hollow, spherical, single-layered blackberry-type structures mediated by the presence of monovalent counterions. The effects on the assembly of changing the solvent polarity and adjusting the pH were further investigated to confirm the presence of electrostatic interactions and hydrogen bonding as the driving forces. Results showed that PPI dendrimers form stable, hollow spheres in 5-20% v/v acetone/water and that the size of the spheres decreases monotonically as the solvent polarity and/or the charge on the dendrimers (i.e., lower solution pH) increases. This is the first example to show that small monovalent counterions can trigger attraction among PPI dendrimers (or broadly defined polyelectrolytes) that is strong enough to bring them together to form large, stable supramolecular assemblies, which indicates that these organic macroions have similar solution behavior to more-well-defined inorganic molecular macroions.

Change of electrostatic potential of mean force between two curved surfaces due to different salt composition, ion valence and size under certain ionic strength

Change of an electrostatic potential of mean force (EPMF) between two cylindrical rod surfaces with salt composition, ion valence, and ion size at a constant ionic strength of 0.3M is studied by a classical density functional theory (CDFT) in a primitive model electrolyte solution. Several novel observations are made: (i) strength of a so-called like charge attraction (LCA) reduces in an invariable manner with the salt solution changing from single 2:1 electrolyte to mixture of 2:1 and 1:1 type electrolytes of varying concentration ratios; the change is even over entire range of the composition variation under low surface charge strength, and tends to be insensitive to the composition variation in the presence of the divalent counter-ion, and more and more drastic at a critical point the divalent counter-ion disappears, respectively, as the surface charge strength becomes big enough. (ii) Both monovalent counter-ion and co-ion diameters have only a marginal effect on both the LCA strength and equilibrium distance, and the former “abnormally” affects less than the latter. (iii) Depending on the surface charge strength considered, the divalent counter-ion diameter influences the LCA strength in solution comprised of 2:1 type and 1:1 type electrolytes, monotonously or non-monotonously. All of these findings provide forceful support for a recently proposed hydrogen-bonding style mechanism explaining the LCA.

Dynamics of a polyelectrolyte under a constant electric field

We perform a molecular dynamics simulation of a polyelectrolyte in a viscous fluid under an external electric field to study the dynamics of gel-free electrophoresis. To incorporate the hydrodynamic effects, we employ a coarse-grained description of water by using multiparticle collision dynamics. We use a screened Coulomb interaction among the monomers and explicit monovalent counterions to model the electrostatic interactions in an ionic solution. The mobility of the polyelectrolyte µ is obtained as a function of the molecular weight N, the electric field strength E,and the Debye screening length of the solvent λ. The mobility is found to be independent of N for large N and to exhibit a maximum at a certain N for a large λ, which are in agreement with experimental results. The dependence of µ on E is also examined and discussed by considering the effects of an electric field on counterion condensation. The dependence of µ on λ shows a discrepancy between our simulation and experiments, which implies that the added salts not only screen out the Coulomb interaction but also participate in the counterion condensation significantly.

Counterion-only electrical double layers: An application of density functional theory.

Within the framework of density functional theory, a self-consistent approach of weighted correlation approximation is developed to give an accurate account of the cross correlations between the Coulombic interaction and the hard-sphere exclusion in the counterion-only electrical double layers. Application of the approach to the cases of practical interest, against the Monte Carlo simulations, shows that it is excellent in describing the structural properties and the pressures of the confined solutions involving both mono- and divalent counterions between two planar charged walls. In particular, the study suggests that the relative importance of electrostatic correlations in comparison to the effects of ionic excluded volume and direct Coulomb interactions depends on the valency of the counterions and the surface charge density. In a clay system with mixed counterions, the competition between the mono- and divalent ions results in a large swelling when the fraction of surface charge compensated by monovalent counterions is greater than 30%. In the opposite situation involving mostly divalent counterions, a limited swelling is found and the attraction between the clay particles favors the formation of stacks incorporating a water layer of about 1.0 nm. These findings are consistent with experimental observations, giving insight into some mechanisms governing the stability of colloidal clay in salt-free or dilute solutions.

Confined polyelectrolytes: The complexity of a simple system.

The interaction between polyelectrolytes and counterions in confined situations and the mutual relationship between chain conformation and ion condensation is an important issue in several areas. In the biological field, it assumes particular relevance in the understanding of the packaging of nucleic acids, which is crucial in the design of gene delivery systems. In this work, a simple coarse-grained model is used to assess the cooperativity between conformational change and ion condensation in spherically confined backbones, with capsides permeable to the counterions. It is seen that the variation on the degree of condensation depends on counterion valence. For monovalent counterions, the degree of condensation passes through a minimum before increasing as the confining space diminishes. In contrast, for trivalent ions, the overall tendency is to decrease the degree of condensation as the confinement space also decreases. Most of the particles reside close to the spherical wall, even for systems in which the density is higher closer to the cavity center. This effect is more pronounced, when monovalent counterions are present. Additionally, there are clear variations in the charge along the concentric layers that cannot be totally ascribed to polyelectrolyte behavior, as shown by decoupling the chain into monomers. If both chain and counterions are confined, the formation of a counterion rich region immediately before the wall is observed. Spool and doughnut-like structures are formed for stiff chains, within a nontrivial evolution with increasing confinement.

Aggregation of Colloidal Particles in the Presence of Multivalent Co-Ions: The Inverse Schulze-Hardy Rule.

Shifts of the critical coagulation concentration (CCC) in particle suspensions in salt solutions containing multivalent co-ions and monovalent counterions are rationalized. One observes that the CCC is inversely proportional to the valence, and this behavior is referred to as the inverse Schulze-Hardy rule. This dependence is established by means of measurements of the stability ratio for positively and negatively charged latex particles with time-resolved light scattering. The same dependence is equally suggested by calculations of the CCC with the Derjaguin, Landau, Verwey, and Overbeek (DLVO) theory, whereby the full Poisson-Boltzmann equation for the asymmetric electrolytes has to be used. The latter aspect is essential, since in the case of multivalent co-ions the surface charge is principally neutralized by monovalent counterions. This rule complements the classical Schulze-Hardy rule, which applies in the case of multivalent counterions, and states that the CCC is inversely proportional to the sixth power of the valence.

Interaction Forces and Aggregation Rates of Colloidal Latex Particles in the Presence of Monovalent Counterions.

Force profiles and aggregation rates involving positively and negatively charged polystyrene latex particles are investigated in monovalent electrolyte solutions, whereby the counterions are varied within the Hofmeister series. The force measurements are carried out with the colloidal probe technique, which is based on the atomic force microscope (AFM), while the aggregation rates are measured with time-resolved multiangle light scattering. The interaction force profiles cannot be described by classical DLVO theory, but an additional attractive short-ranged force must be included. An exponential force profile with a decay length of about 0.5 nm is consistent with the measured forces. Furthermore, the Hamaker constants extracted from the measured force profiles are substantially smaller than the theoretical values calculated from dielectric spectra. The small surface roughness of the latex particles (below 1 nm) is probably responsible for this deviation. Based on the measured force profiles, the aggregation rates can be predicted without adjustable parameters. The measured absolute aggregation rates in the fast regime are somewhat lower than the calculated ones. The critical coagulation concentration (CCC) agrees well with the experiment, including the respective shifts of the CCC within the Hofmeister series. These shifts are particularly pronounced for the positively charged particles. However, the consideration of the additional attractive short-ranged force is essential to quantify these shifts correctly. In the slow regime, the calculated rates are substantially smaller than the experimental ones. This disagreement is probably related to surface charge heterogeneities.

Binding structure and kinetics of surfactin monolayer formed at the air/water interface to counterions: A molecular dynamics simulation study

The binding structure and kinetics of ionized surfactin monolayer formed at the air/water interface to five counterions, Li+, Na+, K+, Ca2+, and Ba2+ (molar ratios of surfactin to monovalent and divalent counterions are 1:2 and 1:1 respectively), have been studied using molecular dynamics simulation. The results show that surfactin exhibits higher binding affinity to divalent counterions, Ca2+, and Ba2+, and smaller monovalent counterion, Li+, than Na+ and K+. Both carboxyl groups in surfactin are accessible for counterions, but the carboxyl group in Glu1 is easier to access by counterions than Asp5. Salt bridges are widely built between carboxyl groups by counterions, and the probability of the formation of intermolecular salt bridge is markedly larger than that of intramolecular salt bridge. Divalent counterions perform well in forming salt bridges between carboxyl groups. The salt bridges mediated by Ca2+ are so rigid that the lifetimes are about 0.13ns, and the break rates of these salt bridges are 1–2 orders of magnitude smaller than those mediated by K+ which is about 5ps in duration. The positions of the hydration layer of carboxyl groups are independent of counterions, but the bound counterions induce the dehydration of carboxyl groups and disturb the hydrogen bonds built between carboxyl group and hydration water.

Communication: Intraparticle segregation of structurally homogeneous polyelectrolyte microgels caused by long-range Coulomb repulsion.

Structurally homogeneous polyelectrolyte microgels in dilute aqueous solutions are shown to exhibit inhomogeneous density profile including intraparticle "phase" coexistence of hollow core and dense "skin." This effect is a consequence of long-range Coulomb repulsion of charged groups which appear because of entropy-driven escape of monovalent counterions into the outer solvent. Excess of the charged groups at the periphery of the microgel particle reduces electrostatic energy and overall free energy of the system despite a penalty in the elastic free energy of strongly stretched subchains in the hole. This finding can serve as additional tool controlling encapsulation, transport, and release of high- and low-molecular-weight species in processes where the microgels are used as delivery systems.

Long-ranged and soft interactions between charged colloidal particles induced by multivalent coions.

Forces between charged particles in aqueous solutions containing multivalent coions and monovalent counterions are studied by the colloidal probe technique. Here, the multivalent ions have the same charge as the particles, which must be contrasted to the frequently studied case where multivalent ions have the opposite sign as the substrate. In the present case, the forces remain repulsive and are dominated by the interactions of the double layers. The valence of the multivalent coion is found to have a profound influence on the shape of the force curve. While for monovalent coions the force profile is exponential down to separations of a few nanometers, the interaction is much softer and longer-ranged in the presence of multivalent coions. The force profiles in the presence of multivalent coions and in the mixtures of monovalent and multivalent coions can be accurately described by Poisson-Boltzmann theory. These results are accurate for different surfaces and even in the case of highly charged particles. This behavior can be explained by the fact that the force profile follows the near-field limit to much larger distances for multivalent coions than for monovalent ones. This limit corresponds to the conditions with no salt, where the coions are expelled between the two surfaces.

Interactions between charged lamellae in aqueous solution.

Interactions between charged surfaces in aqueous solutions, widespread in soft matter and biology, are very complex and, despite many efforts, their full explanation remains challenging. We support the idea that, in contrast to extremely small separations (d≤2 nm), where many effects, prominently those linked to the structure of liquid water, interfere, electrostatics alone rules over larger distances (d≥5 nm) at low ionic strength. We set up specially designed surface force apparatus (SFA) experiments to measure the elastic compressibility modulus of a stack of charged membranes with monovalent counterions, directly and with high precision. We demonstrate that electrostatics alone, if implemented beyond Poisson-Boltzmann theory, fully accounts for the data, nonelectrostatic contributions playing at best a minor role.

Charge Inversion Effects in Electrophoresis of Polyelectrolytes in the Presence of Multivalent Counterions and Transversal Electric Fields

By molecular dynamics simulations we investigate the transport of charged polymers in confinement, under externally applied electric fields, in straight cylinders of uniform diameter and in the presence of monovalent or multivalent counterions. The applied electric field has two components; a longitudinal component along the axis of the cylinder and a transversal component perpendicular to the cylinder axis. The direction of electrophoretic velocity depends on the polyelectrolyte length, valency of the counterions present in solution and transversal electric field value. A statistical model is put forward in order to explain these observations.

Properties of a planar electric double layer under extreme conditions investigated by classical density functional theory and Monte Carlo simulations.

Monte Carlo (MC) simulation and classical density functional theory (DFT) results are reported for the structural and electrostatic properties of a planar electric double layer containing ions having highly asymmetric diameters or valencies under extreme concentration condition. In the applied DFT, for the excess free energy contribution due to the hard sphere repulsion, a recently elaborated extended form of the fundamental measure functional is used, and coupling of Coulombic and short range hard-sphere repulsion is described by a traditional second-order functional perturbation expansion approximation. Comparison between the MC and DFT results indicates that validity interval of the traditional DFT approximation expands to high ion valences running up to 3 and size asymmetry high up to diameter ratio of 4 whether the high valence ions or the large size ion are co- or counter-ions; and to a high bulk electrolyte concentration being close to the upper limit of the electrolyte mole concentration the MC simulation can deal with well. The DFT accuracy dependence on the ion parameters can be self-consistently explained using arguments of liquid state theory, and new EDL phenomena such as overscreening effect due to monovalent counter-ions, extreme layering effect of counter-ions, and appearance of a depletion layer with almost no counter- and co-ions are observed.

Elasticity and mechanical instability of charged lipid bilayers in ionic solutions.

We use coarse-grained Monte Carlo simulations to study the elastic properties of charged membranes in solutions of monovalent and pentavalent counterions. The simulation results of the two cases reveal trends opposite to each other. The bending rigidity and projected area increase with the membrane charge density for monovalent counterions, while they decrease for the pentavalent ions. These observations can be related to the counterion screening of the lipid charges. While the monovalent counterions only weakly screen the Coulomb interactions, which implies a repulsive Coulomb system, the multivalent counterions condense on the membrane and, through spatial charge correlations, make the effective interactions due to the charged lipids attractive. The differences in the elastic properties of the charged membranes in monovalent and multivalent counterion solutions are reflected in the mechanisms leading to their mechanical instability at high charge densities. In the former case, the membranes develop pores to relieve the electrostatic tensile stresses, while in the latter case, the membrane exhibits large wavelength bending instability.

Weak polyelectrolytes in the presence of counterion condensation with ions of variable size and polarizability

.Light scattering and viscometric measurements on weak polyelectrolytes show two important aspects of counterion condensation, namely, non-monotonic variation in the polyelectrolyte size with the increase in the electrostatic strength, and, monovalent counterion selectivity in determining the nature of collapse transition at high electrostatic strengths. Here, we present a self-consistent variational theory for weak polyelectrolytes which includes the effects of the polarizability of monovalent counterions. Our theory reproduces several experimental findings including non-monotonic conformational size with the variation in the electrostatic strength and a shift from a continuous to a discontinuous collapse transition with the increase in the dipole strength of condensed ions. At low dipole strength and high electrostatic strength, our theory predicts a series of solvent quality driven size transitions spanning the re-entrant poor, theta and good solvent regimes. At high dipole strength, the size remains that of a compact globule independent of solvent quality. The dipole strength of the ion-pair formed due to counterion condensation, which depends on the size and polarizability of the monovalent counterions, is found to be an important molecular parameter in determining the nature of collapse transition, and the size of the collapsed state at high electrostatic strength.