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.     

Complexation of ferric oxide particles with pectins of different charge density

The effect of polyelectrolyte charge density on the electrical properties and stability of suspensions of oppositely charged oxide particles is followed by means of electro-optics and electrophoresis. Variations in the electro-optical effect and the electrophoretic mobility are examined at conditions where fully ionized pectins of different charge density adsorb onto particles with ionizable surfaces. The charge neutralization point coincides with the maximum of particle aggregation in all suspensions. We find that the concentration of polyelectrolyte, needed to neutralize the particle charge, decreases with increasing charge density of the pectin. The most highly charged pectin presents an exception to this order, which is explained with a reduction of the effective charge density of this pectin due to condensation of counterions. The presence of condensed counterions, remaining bound to the pectin during its adsorption on the particle surface, is proved by investigation of the frequency behavior of the electro-optical effect at charge reversal of the particle surface.     

Electrophoretic mobility of a highly charged colloidal particle in a solution of general electrolytes.

For a highly charged particle in an electrolyte solution, counterions are condensed very near the particle surface. The electrochemical potential of counterions accumulated near the particle surface is thus not affected by the applied electric field, so that the condensed counterions do not contribute to the particle electrophoretic mobility. In the present paper we derive an expression for the electrophoretic mobility mu(infinity) of a highly charged spherical particle of radius a and zeta potential zeta in the limit of very high zeta in a solution of general electrolytes with large ka (where k is the Debye-Hückel parameter) on the basis of our previous theory for the case of symmetrical electrolytes (H. Ohshima, J. Colloid Interface Sci. 263 (2003) 337). It is shown that zeta can formally be expressed as the sum of two components: the co-ion component, zetaco-ion, and the counterion component, zetacounterion (where zeta = zetaco-ion + zetacounterion) and that the limiting electrophoretic mobility mu(infinity) is given by mu(infinity) = epsilonr epsilon0 zetaco-ion(infinity)/eta + 0(1/ka), where zetaco-ion(infinity) is the high zeta-limiting form of zetaco-ion, epsilonr and eta are, respectively, the relative permittivity and viscosity of the solution, and epsilon0 is the permittivity of a vacuum. That is, the particle behaves as if its zeta potential were zetaco-ion(infinity), independent of zeta. For the case of a positively charged particle in an aqueous electrolyte solution at 25 degrees C, the value of zetaco-ion(infinity) is 35.6 mV for 1-1 electrolytes, 46.0 mV for 2-1 electrolytes, and 12.2 mV for 1-2 electrolytes. It is also found that the magnitude of mu(infinity) increases as the valence of co-ions increases, whereas the magnitude of mu(infinity) decreases as the valence of counterions increases.     

Analysis of the degree of nematic ordering within dense aqueous dispersions of charged anisotropic colloids by 23Na NMR spectroscopy

Aqueous dispersions of Laponite, a synthetic clay neutralized by sodium counterions, are used as a model of charged anisotropic colloids to probe the influence of the shape of the particle on their organization within a macroscopic nematic phase. Because of the large fraction of condensed sodium counterions in the vicinity of the clay particle, (23)Na NMR is a sensitive probe of the nematic ordering of the clay dispersions. We used line shape analysis of the (23)Na NMR spectra and measurements of the Hahn echo attenuation to quantify the degree of alignment of the individual clay particles along a single nematic director. As justified by simple dynamical simulations of the interplay between the sodium quadrupolar relaxation and its diffusion through the porous network limited by the surface of the clay particles, we probe the degree of ordering within these clay nematic dispersions by measuring the variation of the apparent (23)Na NMR relaxation rates as a function of the macroscopic orientation of the clay dispersion within the magnetic field.     

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.     

Corrected Debye-Hückel analysis of surface complexation; III. Spherical particle charging including ion condensation

Statistical mechanics has been used to derive a model for the charging of a spherical particle in a salt solution to complement our experimental studies and gain a deeper understanding of the processes involved in surface complexation. Our chosen model goes beyond the equilibrium constants and the Gouy-Chapmann theory currently used in surface complexation models. The proton adsorption is taken to occur at a harmonic potential well on the surface characterized by a frequency v and a well depth u(0). Outside the particle surface there is a capacitor layer of width w(c) which is impenetrable to the salt ions. The diffuse screening of the charged particle is described by a corrected Debye-Hückel analysis accounting for ion size in the ion-ion interactions. To account also for nonlinear electrostatic response a layer of condensed counterions has been introduced. The criterion for the onset of ion condensation is that the electrostatic field exceeds a linear response criterion. Ion size effects are accounted for in terms of hole-corrected electrostatic energies and excluded volume. The model has been applied to titrated surface charge data on goethite (alpha-FeOOH) at various background concentrations and good agreement between the experimental data and the model was obtained. Both the size of the screening ions and the central particle size were shown to be of importance for the surface charge.     

On the limiting electrophoretic mobility of a highly charged colloidal particle in an electrolyte solution

The electrophoretic mobility of a spherical charged colloidal particle in an electrolyte solution with large kappaa (where kappa= Debye-Hückel parameter and a= particle radius) tends to a nonzero constant value in the limit of high zeta potential. It is demonstrated that this is caused by the fact that counterions condensed near the highly charged particle surface do not contribute to the electrophoretic mobility and only co-ions govern the mobility. A simple method to derive the limiting electrophoretic mobility expression is given. The present method is also applied to cylindrical particles, showing that the leading term of the limiting electrophoretic mobility of a cylindrical particle in a transverse field with large kappaa is the same as that of a spherical particle. The electrophoretic mobility of a cylindrical particle in a tangential field, on the other hand, is proportional to the particle zeta potential and does not exhibit a constant limiting value for high zeta potentials.     

Electric double layer for spherical particles in salt-free concentrated suspensions including ion size effects

The equilibrium electric double layer (EDL) that surrounds colloidal particles is essential for the response of a suspension under a variety of static or alternating external fields. An ideal salt-free suspension is composed of charged colloidal particles and ionic countercharges released by the charging mechanism. Existing macroscopic theoretical models can be improved by incorporating different ionic effects usually neglected in previous mean-field approaches, which are based on the Poisson-Boltzmann equation (PB). The influence of the finite size of the ions seems to be quite promising because it has been shown to predict phenomena like charge reversal, which has been out of the scope of classical PB approximations. In this work we numerically obtain the surface electric potential and the counterion concentration profiles around a charged particle in a concentrated salt-free suspension corrected by the finite size of the counterions. The results show the high importance of such corrections for moderate to high particle charges at every particle volume fraction, especially when a region of closest approach of the counterions to the particle surface is considered. We conclude that finite ion size considerations are obeyed for the development of new theoretical models to study non-equilibrium properties in concentrated colloidal suspensions, particularly salt-free ones with small and highly charged particles.     

Charge renormalization of charged spheres based on thermodynamic properties

At strong electrostatic coupling, counterions are accumulated in the vicinity of the surface of the charged particle with intrinsic charge Z. In order to explain the behavior of highly charged particles, effective charge Z(*) is therefore invoked in the models based on Debye-Huckel approximation, such as the Derjaguin-Landau-Verwey-Overbeek potential. For a salt-free colloidal suspension, we perform Monte Carlo simulations to obtain various thermodynamic properties omega in a spherical Wigner-Seitz cell. The effect of dielectric discontinuity is examined. We show that at the same particle volume fraction, counterions around a highly charged sphere with Z may display the same value of omega as those around a weakly charged sphere with Z(*), i.e., omega(Z)=omega(Z(*)). There exists a maximally attainable value of omega at which Z=Z(*). Defining Z(*) as the effective charge, we find that the effective charge passes through a maximum and declines again due to ion-ion correlation as the number of counterions is increased. The effective charge is even smaller if one adopts the Debye-Huckel expression omega(DH). Our results suggest that charge renormalization can be performed by chemical potential, which may be observed in osmotic pressure measurements.     

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.     

Formation of polyelectrolyte multilayers from polysaccharides at low ionic strength

Layer-by-layer deposition of sodium carboxymethylcellulose (NaCMC) and chitosan (CHI) was used to create polyelectrolyte multilayers on ellipsoidal beta-FeOOH particles at low ionic strength. Using electro-optics, we investigated the formation of films in dependence on the polyelectrolyte charge density by controlling pH of the dipping solutions. We found out a linear growth of the CMC/CHI films when they are constructed from highly charged CHI (at pH 4.0) and weakly charged NaCMC (at pH 4.0 and 5.5). The hydrodynamic thickness of the film constructed at pH 4.0/4.0 is unusually large for a linearly growing film (ca. 220 nm after deposition of 8 bilayers), but it strongly decreases (ca. 4 times) with increasing ionization of NaCMC (at pH 5.5). In both cases, the multilayer buildup proceeded through a series of adsorption-desorption steps. This was explained by a partial loss of CHI from the film surface on exposure to the solution of longer NaCMC molecules. The irregular film growth correlated quite well with the variations in the electrical polarizability of the polymer-coated particles. This correlation enabled us to conclude that the adsorption of both polymers occurs only on the film surface, with no diffusion in and out of the film bulk during deposition of each CMC/CHI bilayer.     

Aspects on the interaction between sodium carboxymethylcellulose and calcium carbonate and the relationship to specific site adsorption

The mechanisms of adsorption and association for sodium carboxymethylcellulose (NaCMC) in calcium carbonate suspensions have been determined from isothermal calorimetry and adsorption measurements. The equilibrium adsorption isotherms were determined by two different methods of separation; a depletion method and a serum exchange method. The enthalpy of dilution for NaCMC was determined on supernatants obtained from the calcium carbonate suspensions in order to investigate the interaction between NaCMC and dissolved species from the mineral. For comparison, NaCMC was injected into CaCl(2) solutions in order to determine the role of calcium ions in the adsorption process. The initial part of the adsorption isotherm showed a quasi-infinite slope indicating a high affinity for the NaCMC to the calcium carbonate surface, which was significantly reduced when anionic sodium polyacrylate was preadsorbed onto the calcium carbonate implying competitive adsorption. An endothermic enthalpy change was observed between the NaCMC and the calcium carbonate surface, suggesting attachment of the carboxylic acid groups onto the hydrated calcium sites. A similar endothermic enthalpy was observed when NaCMC was injected into CaCl(2) solutions or supernatants obtained from the calcium carbonate suspensions, indicating a complexation of carboxylic acid groups and hydrated calcium ions. It was concluded that the mechanisms of interaction of NaCMC in calcium carbonate suspensions are primarily an association between NaCMC and Lewis acid sites on the calcium carbonate surface and the formation of NaCMC-Ca(2+) complexes in the bulk solution, both of which will be affected by the amount of anionic sodium polyacrylate present.     

Varying the counterions at a charged interface

The influence of different counterions on the adsorption behavior of the ionic soluble surfactant dodecyl-dimethylammonium-pyridimium bromide is investigated. The addition of potassium halogenides to aqueous solutions of the surfactant modifies the surface activity of the amphiphile and has a profound influence on the surface tension isotherms. The measured critical micelle concentration follows the order of the periodic table of elements which is in strong contrast to the surface excess. The number density of the adsorbed surfactants at the cmc does not depend on the amount of counterions in the solution but on the nature of the counterion. Furthermore, evidence is provided that the surface region is depleted on fluoride ions. Surface second harmonic generation and ellipsometry have been used to gain direct structural information which complement the thermodynamic considerations. The combination of both optical techniques yields the number density of the condensed counterions within the compact layer. A strategy to retrieve selected parameters of the ion binding model of Radke et al. is presented. The analysis of the optical data reveal the existence of a phase transition towards a surface condensed state with increasing salt condensation.     

Ion adsorption and lamellar-lamellar transitions in charged bilayer systems

Using a primitive model approach, we analyze the influence of ion specific adsorption on the phase behavior of charged lamellar systems. The presence of a weak short-ranged surface potential, attracting monovalent counterions, induces a phase separation, where the separate phases have different repeat distance. If the adsorption potential is very weak, the more narrow phase never forms. An opposite behavior is found for strong surface affinities. Both Monte Carlo simulations and a recently developed correlation-corrected Poisson-Boltzmann theory are adopted, with a nearly quantitative agreement between the approaches. Different counterions are discriminated by the adsorption potential strength, and with physically reasonable values, experimental observations on these systems are well reproduced. The study highlights the importance of electrostatic correlations, even though only monovalent ions are present.     

Simple model for DNA adsorption onto a mica surface in 1:1 and 2:1 electrolyte solutions

We propose a simple theory of interactions between like-charged polyelectrolyte and a surface based on a mean-field Derjaguin-Landau-Verwey-Overbeek approach. It predicts that the van der Waals attractive interactions are responsible for irreversible physisorption of polyelectrolytes onto charged surfaces. We show that monovalent salts contribute significantly to repulsive interactions, while enhancing the attraction very slightly. The effect of the divalent counterions is reverse. Therefore, to achieve the adsorption, the overall repulsion due to 1:1 electrolyte should be counterbalanced by the stronger van der Waals attraction due to the presence of doubly charged counterions in solution. The theory has been validated experimentally against its ability to predict the minimum polymer/surface interaction energy required for the adsorption using DNA/mica in NaCl, MgCl2, and NiCl2 solutions as a test system. The theory explains the mechanism of linear DNA adsorption to a mica surface for different solvent compositions and can be used as a tool for predicting the optimum conditions for AFM experiments on linear polymer systems. The model can also be used to make general conclusions on the conformation of polymer molecules on a surface. We have shown for the DNA/mica surface system that when the adsorption of DNA is mostly governed by long-range van der Waals forces the molecule adopts an ideal 2D conformation. When the adsorption is mostly due to short-range ion-correlation forces, DNA will appear 3D --> 2D projected in agreement with experimental data.     

Anionic polyelectrolyte adsorption on mica mediated by multivalent cations: a solution to DNA imaging by atomic force microscopy under high ionic strengths

Adsorption of DNA molecules on mica, a highly negatively charged surface, mediated by divalent or trivalent cations is considered. By analyzing atomic force microscope (AFM) images of DNA molecules adsorbed on mica, phase diagrams of DNA molecules interacting with a mica surface are established in terms of concentrations of monovalent salt (NaCl) and divalent (MgCl2) or multivalent (spermidine, cobalt hexamine) salts. These diagrams show two transitions between nonadsorption and adsorption. The first one arises when the concentration of multivalent counterions is larger than a limit value, which is not sensitive to the monovalent salt concentration. The second transition is due to the binding competition between monovalent and multivalent counterions. In addition, we develop a model of polyelectrolyte adsorption on like-charged surfaces with multivalent counterions. This model shows that the correlations of the multivalent counterions at the interface between DNA and mica play a critical role. Furthermore, it appears that DNA adsorption takes place when the energy gain in counterion correlations overcomes an energy barrier. This barrier is induced by the entropy loss in confining DNA in a thin adsorbed layer, the entropy loss in the interpenetration of the clouds of mica and DNA counterions, and the electrostatic repulsion between DNA and mica. The analysis of the experimental results provides an estimation of this energy barrier. We then discuss some important issues, including DNA adsorption under physiological conditions.     

Electrophoresis and electric conduction in a salt-free suspension of charged particles

The electrophoresis and electric conduction of a suspension of charged spherical particles in a salt-free solution are analyzed by using a unit cell model. The linearized Poisson-Boltzmann equation (valid for the cases of relatively low surface charge density or high volume fraction of the particles) and Laplace equation are solved for the equilibrium electric potential profile and its perturbation caused by the imposed electric field, respectively, in the fluid containing the counterions only around the particle, and the ionic continuity equation and modified Stokes equations are solved for the electrochemical potential energy and fluid flow fields, respectively. Explicit analytical formulas for the electrophoretic mobility of the particles and effective electric conductivity of the suspension are obtained, and the particle interaction effects on these transport properties are significant and interesting. The scaled zeta potential, electrophoretic mobility, and effective electric conductivity increase monotonically with an increase in the scaled surface charge density of the particles and in general decrease with an increase in the particle volume fraction, keeping each other parameter unchanged. Under the Debye-Hückel approximation, the dependence of the electrophoretic mobility normalized with the surface charge density on the ratio of the particle radius to the Debye screening length and particle volume fraction in a salt-free suspension is same as that in a salt-containing suspension, but the variation of the effective electric conductivity with the particle volume fraction in a salt-free suspension is found to be quite different from that in a suspension containing added electrolyte.     

Effect of Variant Counterions on Stability and Particle Size of Silica Sol

The effects of variant counterions with ionic strength of 0.05, 0.10, 0.20 and 0.25 mol·kg^-1 on the stability and particle size of silica sols have been studied using the traditional methods of Ubbelohde viscosity measurement, TEM and titration respectively, finding that the stability and particle size of the silica sols are all concerned with the acidic, positively electric properties and the sizes of the counterions, as well as the attraction between the counterions and surface silicon hydroxyl groups of the silica sols. The small positively charged counterions lead to the decrease in particle sizes, making the silica sol the most stable. But the larger weakly acidic counterions can restrict the particle sizes of the silica sols and easily make the sols coagulate. It was also found that there existed a linear relationship between log r and log η, which has not ever been reported. The effect of temperature on the stability and particle sizes was also discussed.     

dc Electrokinetics for spherical particles in salt-free concentrated suspensions including ion size effects

We study the electrophoretic mobility of spherical particles and the electrical conductivity in salt-free concentrated suspensions including finite ion size effects. An ideal salt-free suspension is composed of just charged colloidal particles and the added counterions that counterbalance their surface charge. In a very recent paper [Roa et al., Phys. Chem. Chem. Phys., 2011, 13, 3960-3968] we presented a model for the equilibrium electric double layer for this kind of suspensions considering the size of the counterions, and now we extend this work to analyze the response of the suspension under a static external electric field. The numerical results show the high importance of such corrections for moderate to high particle charges, especially when a region of closest approach of the counterions to the particle surface is considered. The present work sets the basis for further theoretical models with finite ion size corrections, concerning particularly the ac electrokinetics and rheology of such systems.     

SANS and SAXS analysis of charged nanoparticle adsorption at oil-water interfaces

A systematic study of the adsorption of charged nanoparticles at dispersed oil-in-water emulsion interfaces is presented. The interaction potentials for negatively charged hexadecane droplets with anionic polystyrene latex particles or cationic gold particles are calculated using DLVO theory. Calculations demonstrate that increased ionic strength decreases the decay length of the electrostatic repulsion leading to enhanced particle adsorption. For the case of anionic PS latex particles, the energy barrier for particle adsorption is also reduced when the surface charge is neutralized through changes in pH. Complementary small-angle scattering experiments show that the highest particle adsorption for PS latex occurs at moderate ionic strength and low pH. For cationic gold particles, simple DLVO calculations also explain scattering results showing that the highest particle adsorption occurs at neutral pH due to the electrostatic attraction between oppositely charged surfaces. This work demonstrates that surface charges of particles and oil droplets are critical parameters to consider when engineering particle-stabilized emulsions.