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.     

Surface conductivity reveals counterion condensation within grafted polyelectrolyte layers

Surface conductivity (SC) has been demonstrated to be a valuable parameter for the characterization of surface-bound polyelectrolyte layers (PLs). The measurement of the SC in dependence of the pH and solution concentration yields information about the Donnan potential, PsiD, the intrinsic charge, the potential of the PL electrolyte interface, Psi0, the pK of the ionizable groups within the PLs, and the concentration of segments, n. We discuss herein that SC measurements may additionally provide information about counterion condensation. The mobility of the counterions within grafted poly(acrylic acid) (PAA) layers was estimated from the density of COOH groups and SC data to be only 14% of that of free ions (Zimmermann, et al. Langmuir 2005, 21, 5108). In view of this large deviation and the limited sterical constraints within the brushes, we conclude that the number of freely moving counterions is decreased due to counterion condensation. This interpretation agrees well with the measurement of the osmotic pressure for PAA solution (Boisvert, et al. Polymer 2002, 43, 141), which can be exclusively attributed to the remaining mobile counterions of the polyelectrolyte.     

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.     

Counterion condensation in hydrosols of single-crystalline detonation nanodiamond particles obtained by air annealing of their agglomerates

The pattern of previously recorded dependences of the specific surface charge and electrophoretic mobility of monodisperse detonation nanodiamond particles on pH of aqueous KCl solutions suggests that counterions are condensed on the particle surface. Counterion condensation is considered in terms of the Levin model, and the experimental ratios between the densities of the electrokinetic and surface charges of dispersed particles, as well as the fractions of condensed counterions, are calculated as depending on pH and KCl concentration in nanodiamond hydrosols. The obtained dependences lead to the conclusion that counterion condensation on the surface of detonation nanodiamond particles does indeed take place.     

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.     

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. © 2015 Wiley Periodicals, Inc.     

Transport,and thermodynamic investigations on sodium polystyrenesulfonate in ethylene glycol–water media

Polyion–counterion interactions in sodium polystyrenesulfonate dissolved in (ethylene glycol + water) mixed solvent media have been investigated conductometrically with special reference to their variations as functions of polyelectrolyte concentration, relative permittivity and temperature. Manning counterion condensation theory for polyelectrolyte solutions failed to describe the present experimental results. The data have, therefore, been analyzed using a new model for semidilute polyelectrolyte conductivity which takes into account the scaling arguments proposed by Dobrynin et al. The fractions of uncondensed counterions were found to depend on the polyelectrolyte concentration varying from 0.27 to 0.37, within the concentration range investigated here, indicating a strong interaction between counterions and polyion. A considerable fraction of the counterions is shown to migrate in the same direction as the polyions. The results further demonstrate that the monomer units experience more frictional resistance in solutions as the ethylene glycol content of the mixture increases or as the temperature decreases.     

Counterion release from adsorbed highly charged polyelectrolyte: an electrooptical study

The adsorption of sodium poly(4-styrene sulfonate) on oppositely charged beta-FeOOH particles is studied by electrooptics. The focus of this paper is on the release of condensed counterions from adsorbed polyelectrolyte upon surface charge overcompensation. The fraction of condensed Na+ counterions on the adsorbed polyion surface is estimated according to the theory of Sens and Joanny and it is compared with the fraction of condensed counterions on nonadsorbed polyelectrolyte. The relaxation frequency of the electrooptical effect from the polymer-coated particle is found to depend on the polyelectrolyte molecular weight. This is attributed to polarization of the layer from condensed counterions on the polyion surface, being responsible for creation of the effect from particles covered with highly charged polyelectrolyte. The number of the adsorbed chains is calculated also assuming counterion condensation on the adsorbed polyelectrolyte and semiquantative agreement is found with the result obtained from the condensed counterion polarizability of the polymer-coated particle. Our findings are in line with theoretical predictions that the fraction of condensed counterions remains unchanged due to the adsorption of highly charged polyelectrolyte onto weakly charged substrate.     

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   

Numerical calculation of the electrophoretic mobility of a spherical particle in a salt-free medium

By extending an approximate theory of the electrophoretic mobility of dilute spherical colloidal particles in a salt-free medium containing only counterions (H. Ohshima, J. Colloid Interface Sci. 248 (2002) 499--503), a systematic numerical method is given for the calculation of the electrophoretic mobility, which is based on an iteration method. We assume that each sphere is surrounded by a spherical free volume, within which counterions are distributed so that electro-neutrality is satisfied. The electrophoretic mobility is found to be determined mainly by the pressure due to the counterions at the outer surface of the free volume. It is shown how the mobility values deviate from those expected from Hückel's formula for high particle charges or zeta potentials because of the counterion condensation effect.     

Molecular dynamics and neutron scattering study of the dependence of polyelectrolyte dendrimer conformation on counterion behavior

Atomistic molecular dynamics (MD) simulations and contrast variation small angle neutron scattering (SANS) have been combined to investigate the Generation-5 polyelectrolyte polyamidoamine starburst dendrimer. This work reveals the dendrimer conformational dependence on counterion association at different levels of molecular charge. The accuracy of the simulations is verified through satisfactory comparison between modeled results, such as excess intra-dendrimer scattering length density distribution and hydration level, and their experimental counterparts. While the counterion distributions are not directly measureable with SANS, the spatial distribution of the counterions and their dendrimer association are extracted from the validated MD equilibrium trajectories. It is found that the conformation of the charged dendrimer is strongly dependent on the counterion association. Sensitivity of the distribution of counterions around charged amines to the counterion valency is qualitatively explained by adopting Langmuir adsorption theory. Moreover, via extending the concept of electrical double layer for compact charged colloids, we define an effective radius of a charged dendrimer including the spatial distribution of counterions in its vicinity. Within the same framework, the correlation between the strength of intra-dendrimer electrostatic repulsion and the counterion valency and dynamics is also addressed.     

Monte Carlo simulations of charged dendrimer-linear polyelectrolyte complexes and explicit counterions

We study complexes composed of one dendrimer of generation G = 4 (G4 dendrimer) with N(t) = 32 charged terminal groups and an oppositely charged linear polyelectrolyte accompanied by neutralizing counterions in an athermal solvent using Monte Carlo simulations based on the bond fluctuation model. In our study both the full Coulomb potential and the excluded volume interactions are taken into account explicitly with the reduced temperature τ and the chain length N(ch) as the main simulation parameters. Our calculations indicate that there exist three temperature ranges that determine the behavior of such complexes. At τ(complex) stable charged dendrimer-linear polyelectrolyte complexes are formed first, which are subsequently accompanied by selective counterion localization within the complex interior at τ(loc) ≤ τ(complex), and counterion condensation as temperature is further decreased below τ(cond) < τ(loc). In particular, we observe that condensation takes place exclusively on the excess charges in the complex and thus no condensation is observed at the compensation point (N(ch) = N(t)), irrespective of τ. For N(ch) ≠ N(t) the complex is overally charged. Furthermore, we discuss the size and structure of the dendrimer and the linear polyelectrolyte within the complex, as well as spatial distributions of monomers and counterions. Conformations of the chain in the bound state are analysed in terms of loops, trains, and tails.     

Electrophoretic evidence for a new type of counterion condensation

A systematic capillary electrophoresis study uncovered how polyelectrolyte effective charge density varies with backbone charge spacing and solvent dielectric constant. The study primarily focused on aliphatic ionenes, a special class of polyelectrolytes, which possess regularly spaced quaternary ammonium groups in the backbone. Complete ionization of functional units and good solvency in water or mixtures of water with lower dielectric constant solvents (methanol, acetonitrile) enabled continuous measurements of ionene effective charge density through the onset of counterion condensation. Ionenes with both uniform and alternating charge spacing were examined. As expected, effective charge density rose linearly with fixed charge density to a critical value, above which effective charge density remained constant. Deviating from expectation, the onset of condensation did not occur at a critical fixed charge density. Instead, condensation initiated at a constant critical Bjerrum length. The same onset condition was found for quaternized poly(vinyl pyridine)s. These experimental results suggest a new form of condensation, one driven by ion-pairing of polyelectrolyte with counterions. In support of this hypothesis, the onset of condensation appeared to correlate with counterion size. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 3616–3627, 2004     

Phosphate binding to the [Au(IPr)] moiety: inner vs. outer sphere coordination behaviour

The synthesis and characterization of a new class of cationic (NHC)gold(I) (NHC = N-Heterocyclic carbene) complex containing the phosphate counterions TRISPHAT and TRISPHAT-N have been achieved. The selection of the appropriate hexacoordinated phosphate architecture permits the isolation of complexes bearing an inner or outer sphere anionic counterion.     

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 studies of anchored polyelectrolytes

We study polyelectrolytes end-grafted to a surface in a model which includes counterions explicitly and treats the full long-range Coulomb interaction. For strongly charged polyelectrolytes the counterions are localized inside the brush and electroneutrality is satisfied locally. Under these conditions, we find that the brush thickness is linearly proportional to the chain length and the grafting density. The counterion distribution is strongly inhomogeneous, and counterion condensation can be observed although the Bjerrum length is smaller than the average bond length. Varying the Bjerrum length we find a non-monotonic behaviour of the brush height. Counterion diffusion is anisotropic, and is enhanced at higher grafting densities. For partially charged polyelectrolytes we obtain a crossover from quasi-neutral behaviour to the strongly charged behaviour reported above.     

Influence of mixed and multivalent counterions in overcharging of DNA-like spherocylindrical macroions

The influence of multivalent and mixed valency counterions on the ground-state energetics of overscreening of a core DNA-like model (sphero)cylindrical macroion is investigated using an earlier developed energy minimization numerical simulation algorithm. The effects of mono-, di-, tri-, and tetravalent counterions, and mixed valency (mono- plus di-) counterions are compared and contrasted. It is seen that the depth of the minimum in the excess ground-state energy (over the neutral reference state) versus the number of overcharging counterions increases as counterion valency changes from mono- to tetra- testifying to the efficiency of the overcharging process due to multivalent counterions. The influence of (i) the presence of mixed valency counterions and (ii) counterion size on the energetics is also investigated.     

Line of charges in electrolyte solution near a half-space I. Counterion condensation

The effect of a half-space on counterion condensation around a line of charges in electrolyte solution is examined in the framework of Debye-Hückel electrostatics. The half-space substrate is allowed to be a conductor, a dielectric, or a semiconductor. Counterions are predicted to be released completely as the line of charges approaches a conducting substrate. When it approaches a dielectric substrate, depending on the ratio of solvent to substrate dielectric constant, there are three possibilities: (1) epsilon(sol)/epsilon(sub) < 1; the counterions are partially (or completely) released; (2) epsilon(sol)/epsilon(sub) = 1; the amount of condensation remains unchanged; and (3) epsilon(sol)/epsilon(sub) > 1; more counterions condense. Depending on the relative magnitude of screening lengths in the semiconductor and in the solution, its effect on condensation follows either that of a metal or that of a dielectric. For the case of a moderately doped silicon substrate, condensation is predicted to be similar to that for a dielectric.     

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.