Counterion condensation and release in micellar solutions

Counterion condensation and release in micellar solutions are investigated by direct measurement of counterion concentration with ion-selective electrode. Monte Carlo simulations based on the cell model are also performed to analyze the experimental results. The degree of counterion condensation is indicated by the concentration ratio of counterions in the bulk to the total ionic surfactant added, alpha< or =1. The ionic surfactant is completely dissociated below the critical micelle concentration (cmc). However, as cmc is exceeded, the free counterion ratio alpha declines with increasing the surfactant concentration and approaches an asymptotic value owing to counterion condensation to the surface of the highly charged micelles. Micelle formation leads to much stronger electrostatic attraction between the counterion and the highly charged sphere in comparison to the attraction of single surfactant ion with its counterion. A simple model is developed to obtain the true degree of ionization, which agrees with our Monte Carlo results. Upon addition of neutral polymer or monovalent salts, some of the surfactant counterions are released to the bulk. The former is due to the decrease of the intrinsic charge (smaller aggregation number) and the degree of ionization is increased. The latter is attributed to competitive counterion condensation, which follows the Hefmeister series. This consequence indicates that the specific ion effect plays an important role next to the electrostatic attraction.     

Simulation Study of the Conformational Properties of Diblock Polyelectrolytes in Salt Solutions

Coarse-grained molecular dynamics simulations are performed to understand the behavior of diblock polyelectrolytes in solutions of divalent salt by studying the conformations of chains over a wide range of salt concentrations. The polymer molecules are modeled as bead spring chains with different charged fractions and the counterions and salt ions are incorporated explicitly. Upon addition of a divalent salt, the salt cations replace the monovalent counterions, and the condensation of divalent salt cations onto the polyelectrolyte increases, and the chains favor to collapse. The condensation of ions changes with the salt concentration and depends on the charged fraction. Also, the degree of collapse at a given salt concentration changes with the increasing valency of the counterion due to the bridging effect. As a quantitative measure of the distribution of counterions around the polyelectrolyte chain, we study the radial distribution function between monomers on different polyelectrolytes and the counterions inside the counterion worm surrounding a polymer chain at different concentrations of the divalent salt. Our simulation results show a strong dependence of salt concentration on the conformational properties of diblock copolymers and indicate that it can tune the self-assembly behaviors of such charged polyelectrolyte block copolymers.     

Molecular dynamics simulations of end‐grafted polymers with charged side chains

We report molecular dynamics simulations on bottle‐brush polyelectrolytes end‐grafted to a planar surface. For each bottle‐brush polyelectrolyte, flexible charged side chains are anchored to one neutral main chain. The effects of the counterion valence and the grafting density on the density profiles and the structural characteristics of the brush were studied in this work. It is found that the electrostatic repulsion between charged monomers in the side chains leads an extended conformation of the brush in a solution containing monovalent counterions, while strong electrostatic binding of multivalent counterions to the side chains has a significant contribution to the collapse of the brush. For the trivalent case, the distribution of end monomers in the main chains becomes broader upon decreasing the grafting density, as compared with the monovalent case. However, the position of the distribution for the monovalent case is relatively insensitive to the change of the grafting density. Additionally, with increased counterion valence, enhanced electrostatic correlation between counterions and charged side chains also weakens the diffusive ability of counterions. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Molecular dynamics simulation of discontinuous volume phase transitions in highly-charged crosslinked polyelectrolyte networks with explicit counterions in good solvent

The volumetric properties of highly-charged defect-free polyelectrolyte networks with tetrafunctional crosslinks are studied through molecular dynamics simulations in the canonical ensemble. The network backbone monomers, which are monovalent, and the counterions, which are mono-, di-, or trivalent, are modeled explicitly in the simulations, but the solvent is treated implicitly as a dielectric medium of good solvation quality. The osmotic pressure of the network-solvent system is found to depend greatly on the strength of electrostatic interactions. Discontinuous volume phase transitions are observed when the electrostatic interactions are strong, and the onset of these transitions shifts to higher solvent dielectricity as the counterion valency increases. The roles of the various virial contributions to the osmotic pressure are examined. The network elasticity entropy is found to behave nearly classically. As the network contracts and collapses with increasing strength of electrostatic interactions, the loss of counterion entropy leads to increased counterion osmotic pressure contributions via two mechanisms. The reduction in available configurational space increases the counterion translational entropy contribution to the ideal part of the osmotic pressure, and the greater number of counterion-monomer contacts formed due to counterion condensation and confinement increases the counterion excluded-volume entropy contribution to the excess part of the osmotic pressure. These observations contrast the decrease in the single ideal-gas-like counterion translational entropy contribution to the osmotic pressure predicted by the counterion condensation-charge renormalization theory. An accompanying decrease in the total electrostatic energy balances the loss of counterion excluded-volume entropy as the polyelectrolyte networks collapse in low-dielectric solvents. This interplay between the electrostatic energy and the counterion excluded-volume entropy appears to be responsible for the discontinuous volume phase transitions that are observed in polyelectrolyte networks. The structure of the polyelectrolyte network is also found to be affine in the swollen state, with constituent chains nearly fully extended, and nonaffine in the collapsed state, with the chains adopting a Gaussian conformation.     

Explicit ions condensation around strongly charged polyelectrolytes and spherical macroions: the influence of salt concentration and chain linear charge density. Monte Carlo simulations

The condensation of monovalent counterions and trivalent salt particles around strong rigid and flexible polyelectrolyte chains as well as spherical macroions is investigated by Monte Carlo simulations. The results are compared with the condensation theory proposed by Manning. Considering flexible polyelectrolyte chains, the presence of trivalent salt is found to play an important role by promoting chain collapse. The attraction of counterions and salt particles near the polyelectrolyte chains is found to be strongly dependent on the chain linear charge density with a more important condensation at high values. When trivalent salt is added in a solution containing monovalent salt, the trivalent cations progressively replace the monovalent counterions. Ion condensation around flexible chains is also found to be more efficient compared with rigid rods due to monomer rearrangement around counterions and salt cations. In the case of spherical macroions, it is found that a fraction of their bare charge is neutralized by counterions and salt cations. The decrease of the Debye length, and thus the increase of salt concentration, promotes the attraction of counterions and salt particles at the macroion surface. Excluded volume effects are also found to significantly influence the condensation process, which is found to be more important by decreasing the ion size.     

Excluded volume driven counterion condensation inside nanotubes in a concave electrical double layer model

The physical properties of organic nanotubes attract increasing attention due to their potential benefit in technology, biology and medicine. We study the effect of ion size on the electrical properties of cylindrical nanotubes filled with electrolyte solution within a modified Poisson-Boltzmann (PB) approach. For comparison purposes, small hollow nanospheres filled with electrolyte solution are considered. The finite size of the particles in the inner electrolyte solution is described by the excluded volume effect within a lattice statistics approach. We found that an increased ion size reduces the number of counterions near the charged inner surface of the nanotube, leading to an enlarged electrostatic surface potential. The concentration of counterions close to the inner surface saturates for higher surface charge densities and larger ions. In the case of saturation, the closest counterion packing is achieved, all lattice sites near the surface are occupied and an actual counterion condensation is observed. By contrast, the counterion concentration at the axis of the nanotube steadily increases with increasing surface charge density. This growth is more pronounced for smaller nanotube radii and larger ions. At larger nanotube radii for small ion size counterion condensation may also be observed according to the Tsao criterion, i.e. the counterion concentration at the centre is independent of the number of counterions in the system. With decreasing radius the Tsao condensation effect is shifted towards physiologically unrealistic surface charge densities.     

Theory of competitive counterion adsorption on flexible polyelectrolytes: divalent salts

The counterion distribution around an isolated flexible polyelectrolyte in the presence of a divalent salt is evaluated using the adsorption model [M. Muthukumar, J. Chem. Phys. 120, 9343 (2004)] that considers the Bjerrum length, salt concentration, and local dielectric heterogeneity as physical variables in the system. Self-consistent calculations of effective charge and size of the polymer show that divalent counterions replace condensed monovalent counterions in competitive adsorption. The theory further predicts that at modest physical conditions for a flexible polyelectrolytes such as sodium polystyrene sulfonate in aqueous solutions polymer charge is compensated and reversed with increasing divalent salt. Consequently, the polyelectrolyte shrinks and reswells. Lower temperatures and higher degrees of dielectric heterogeneity between chain backbone and solvent enhance condensation of all species of ions. Complete diagrams of states for the effective charge calculated as functions of the Coulomb strength and salt concentration suggest that (a) overcharging requires a minimum Coulomb strength and (b) progressively higher presence of salt recharges the polymer due to either electrostatic screening (for low Coulomb strengths) or coion condensation (for high Coulomb strengths). Consideration of ion-bridging by divalent counterions leads to a first-order collapse of polyelectrolytes in modest presence of divalent salts and at higher Coulomb strengths. The authors' theoretical predictions are in agreement with the generic results from experiments and simulations.     

Entropic effects in the electric double layer of model colloids with size-asymmetric monovalent ions

The structure of the electric double layer of charged nanoparticles and colloids in monovalent salts is crucial to determine their thermodynamics, solubility, and polyion adsorption. In this work, we explore the double layer structure and the possibility of charge reversal in relation to the size of both counterions and coions. We examine systems with various size-ratios between counterions and coions (ion size asymmetries) as well as different total ion volume fractions. Using Monte Carlo simulations and integral equations of a primitive-model electric double layer, we determine the highest charge neutralization and electrostatic screening near the electrified surface. Specifically, for two binary monovalent electrolytes with the same counterion properties but differing only in the coion's size surrounding a charged nanoparticle, the one with largest coion size is found to have the largest charge neutralization and screening. That is, in size-asymmetric double layers with a given counterion's size the excluded volume of the coions dictates the adsorption of the ionic charge close to the colloidal surface for monovalent salts. Furthermore, we demonstrate that charge reversal can occur at low surface charge densities, given a large enough total ion concentration, for systems of monovalent salts in a wide range of ion size asymmetries. In addition, we find a non-monotonic behavior for the corresponding maximum charge reversal, as a function of the colloidal bare charge. We also find that the reversal effect disappears for binary salts with large-size counterions and small-size coions at high surface charge densities. Lastly, we observe a good agreement between results from both Monte Carlo simulations and the integral equation theory across different colloidal charge densities and 1:1-electrolytes with different ion sizes.     

Affinity interactions in counterion‐polyelectrolyte systems: Competition between different counterions

Non‐bonding, specific interactions between linear polyelectrolytes and different species of counterions (of equal or different valence) are considered in the framework of the counterion condensation theory. It is assumed that these interactions are of short distance nature and that, within our theoretical approach, they apply only to the counterions territorially associated (condensed) to the polyion, which are free to move within the condensation volume V_p around it. It is found that a simple additive term in the total free energy is sufficient to account for this interaction, resulting in a modulation of the polyelectrolytically determined population of territorially bound counterions. The distribution of free and condensed counterions as well as its variation with the physicochemical variables of the solution can be readily calculated. Analysis of literature data on titrations of poly(methacrylic acid) and dextran sulfate in aqueous solution with different species of monovalent and divalent counterions show that both polyanions appear to have a modest affinity free energy (of about RT) for Ca⁺⁺ counterions when compared with Na⁺. On the other hand, polyion interactions with the Mg⁺⁺/Na⁺ pair are well described by bare polyelectrolytic interactions.     

A three‐state model for counterions in a dilute solution of weakly charged polyelectrolytes

In this paper we consider the influence of counterion distribution on the behavior of polyelectrolyte systems. We propose the unified model to describe and to compare the swelling and collapse properties of single polyelectrolyte chains in dilute solutions, microgel particles of various molecular masses, and (as a limiting case) macroscopic gels. A novel feature of the new approach is that we distinguish three possible states of counterions: free counterions inside and outside the polymer macromolecule and a bound state of counterions forming ion pairs with corresponding ions of polymer chains. The latter possibility becomes progressively important when macromolecules or gels shrink. In this case the formation of a supercollapsed state is possible, when all couterions are trapped and form ion pairs. On the other hand, the fact that counterions can float in the outer solution affects essentially the conformation of polyelectrolyte chains in dilute solutions of good quality where practically all counter ions can escape the space inside polymer coils and the repulsion between uncompensated charges plays an important role in the chain behavior.     

The wall and multivalent counterion effects on the electrostatic force between like-charged spherical particles confined in a charged pore

The effect of wall confinement (wall charge and wall-sphere separation distance) on the electrostatic force between two charged spheres confined in a long charged pore in symmetric and asymmetric electrolytes have been quantified by solving the nonlinear Poisson-Boltzmann equation (PBE), using adaptive finite elements combined with error minimization techniques. The computed force indicated the strong effect of the wall potential on the reduction of the repulsive force for all type of electrolytes. The influence of the wall effect was reduced when the valence of the electrolyte was increased. A significant reduction in the repulsive force between the two spheres was also observed when the distance between the pore wall and the sphere surface was reduced. A smaller long-range repulsive interaction was observed between spheres when the solutions contained multivalent counterions as compared with a monovalent solution. However, at short ranges of separation distances multivalent counterions increase the electrostatic repulsive force between the spheres. The effect of the dimensionless radius of the spheres on the electrostatic force between them has been determined and a significant reduction observed as the dimensionless radius was reduced.     

Counterion condensation on charged spheres, cylinders, and planes

We use the framework of counterion condensation theory, in which deviations from linear electrostatics are ascribed to charge renormalization caused by collapse of counterions from the ion atmosphere, to explore the possibility of condensation on charged spheres, cylinders, and planes immersed in dilute solutions of simple salt. In the limit of zero concentration of salt, we obtain Zimm-Le Bret behavior: a sphere condenses none of its counterions regardless of surface charge density, a cylinder with charge density above a threshold value condenses a fraction of its counterions, and a plane of any charge density condenses all of its counterions. The response in dilute but nonzero salt concentrations is different. Spheres, cylinders, and planes all exhibit critical surface charge densities separating a regime of counterion condensation from states with no condensed counterions. The critical charge densities depend on salt concentration, except for the case of a thin cylinder, which exhibits the invariant criticality familiar from polyelectrolyte theory.     

Ion condensation onto self‐assembled nanofibers

Self‐assembled peptide amphiphile (PA) nanofibers are a class of supramolecular materials with promising applications in nanotechnology. Alignment of nanofibers, which is essential for biomaterials applications, is achieved at low salt concentrations in the PA nanofiber suspensions. Regardless of its importance, the effect of ion concentration on the properties of these nanostructures remains unexplored. Using atomistic molecular dynamics simulations, canonical PA nanostructures are investigated to elucidate the relationship between counterion condensation and morphological changes. Simulations reveal that nanofibers with the highest cross‐section density have expanded radii. This expansion decreases the accessible volume for sodium counterions and diminishes the counterion translational entropy, while also reducing the total electrostatic potential. Interestingly, we show that the competition between these effects leads to a fraction of condensed counterions independent of the fiber radius. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 901–906     

New experiments for the quantification of counterion condensation

The condensation of counterions is an important aspect of charged macromolecules. Therefore an experimental characterization of the condensation of counterions is desirable. In this contribution two experimental techniques for the characterization of counterion condensation are introduced and compared: Anomalous Small Angle X-Ray Scattering (ASAXS) is able to probe the spatial distribution of counterions and electrophoresis nuclear magnetic resonance (NMR) measures counterion condensation via the effective charge obtained from the dynamic behaviour of molecules and complexes in an electric field.     

Interaction of cationic surfactants with carboxymethylcellulose in aqueous media

We have examined the polymer-surfactant interaction in mixed solutions of the cationic surfactants, i.e., dodecyltrimethylammonium chloride, dodecyltrimethylammonium bromide, tetradecyltrimethylammonium bromide, hexadecyltrimethylammonium bromide, tetradecyltriphenylphosphonium bromide, and tetradecylpyridinium bromide and a semiflexible anionic polyelectrolyte carboxymethylcellulose in water and aqueous salt solutions by various techniques: tensiometry, viscosimetry or ion-selective electrode method, and dynamic light scattering. We have investigated the effect of varying surfactant chain length, head group size, counterion, and ionic strength on the critical aggregation concentration (CAC) of mixed polymer surfactant systems and the collapse of the polymer molecule under different solution conditions. The CAC decreases with increasing alkyl chain length. Above a certain surfactant concentration, mixed aggregates start growing until their macroscopic phase separation. The growth is more rapid with greater surfactant tail length and with increasing head group size. This is attributed in both cases to the increasing hydrophobic interaction between polymer and surfactant. Among surfactants with monovalent halide counterions, iodide induces the strongest binding, reflected by the onset of growth of the mixed aggregates at low surfactant concentration. This is perhaps related to the decreasing hydration of the counterion from chloride to iodide. The surfactant concentration at which the viscosity of the solution starts to decrease sharply is smaller than the CAC, and probably reflects polymer chain shrinkage due to noncooperative binding.     

Influence of the diffuse layer overcharging or undercharging on the stability of charged interfaces: a restricted grand canonical Monte Carlo study

We have applied a restricted grand canonical Monte Carlo procedure to describe, in the framework of the primitive model, the counterion exchange mechanism between diffuse layers of counterions surrounding segregated charged lamellae. The net charge transfer between the dense and dilute domains is shown to vary as a function of the valence of the neutralizing counterions: undercharging of the dense interlayer is detected in the presence of monovalent counterions and overcharging with divalent counterions. Furthermore, no net reduction of the swelling pressure is detected for monovalent counterions, while a large enhancement of the net interlamellar attraction is found for charged lamellae neutralized by divalent counterions.     

Anomalous small angle x-ray scattering determination of ion distribution around a polyelectrolyte biopolymer in salt solution

The distribution of counterions in solutions of high molecular mass hyaluronic acid, in near-physiological conditions where mono- and divalent ions are simultaneously present, is studied by small angle neutron scattering and anomalous small angle x-ray scattering. The solutions contain either sodium or rubidium chloride together with varying concentrations of calcium or strontium chloride. The effects of monovalent-divalent ion exchange dominate the amplitude and the form of the counterion cloud. In the absence of divalent ions, the shape of the anomalous scattering signal from the monovalent ions is consistent with the distribution calculated from the Poisson-Boltzmann equation, as found by other workers. In mixtures of monovalent and divalent ions, however, as the divalent ion concentration increases, both the diameter and the amplitude of the monovalent ion cloud decrease. The divalent counterions always occupy the immediate neighborhood of the charged polyanion. Above a given concentration their anomalous scattering signal saturates. Even in a large excess of divalent ions, ion exchange is incomplete.     

Presence or absence of counterion specificity in the interaction of alkylammonium surfactants with alkylacrylamide gels

Patterns in the interaction of cationic surfactants with nonionic polymer gels, which were inferred from a recent study from our laboratory, are confirmed by measurements of a series of alkylammonium surfactants with different counterions with a series of alkyl acrylamide gels of increasing hydrophobicity. Two swelling patterns were observed: Either the swelling continued above the surfactant critical micelle concentration (cmc) and the maximum swelling differed for different counterions and increased in the order of Br-相似文献   

Ion aggregation in polymer gels

This brief review deals with our early experimental studies of ion aggregation in polymer gels proceeding via the condensation of counterions on the oppositely charged monomer units of the network with the formation of ion pairs and their clustering into multiplets. The two particular cases of the emergence of ion aggregates are considered: (a) for monovalent counterions in media of low polarity and (b) for multivalent counterions in water.